52 results

volume - quantity of 3-dimensional space

A cereal box has dimensions of 12" x 3" x 18". How many square inches of cardboard are used in its c

A cereal box has dimensions of 12" x 3" x 18". How many square inches of cardboard are used in its construction?
A cereal box is a rectangular solid. The volume formula is V = lwh.
Substituting these values of the cereal box in, we have:
V = 12(3)(18)
V = [B]648 cubic inches[/B]

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the ballon increasing when the radius is 2cm?
[U]The volume (V) of the balloon with radius (r) is:[/U]
V = 4/3πr^3
[U]Differentiating with respect to t, we get:[/U]
dV/dt = 4/3π * 3r^2 * dr/dt
dV/dt = 4πr^2 * dr/dt
The rate of change of the volume is:
dV/dt = 10cm^3s^−1
[U]So, we find dr/dt:[/U]
dr/dt = 1/4πr^2 * dV/dt
dr/dt = 10/4πr^2
dr/dt = 5/2πr^2
Therefore, dr/dt(2cm) is:
dr/dt(2cm) = 5/2π(2)^2
dr/dt(2cm) = 5/2π4
dr/dt(2cm) = [B]5π/8[/B]

A cube has an edge that is x cm long. What is the capacity of C(x)?

A cube has an edge that is x cm long. What is the capacity of C(x)?
Capacity is another word for volume, or the amount an object will hold. Given a side x, the capacity (volume) of a cube is:
C(x) = [B]x^3[/B]

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box?
Since 1 foot = 12 inches, we have:
2 feet 4 inches = 2(12) + 4
2 feet 4 inches = 24 + 4
2 feet 4 inches = 28 inches
We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get:
V = [B]21952 cubic inches[/B]

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v to find the volume. What was the volume of the tank?
1/2 foot = 6 inches
v = (6)^3
v = [B]216 cubic inches[/B]

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of l

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of lead in it.
A lead pipe is a cylinder. We want the volume of a cylinder.
Convert 20ft to inches:
20ft = 12(20) = 240 inches
Find the inner radius:
1/2 * inner diameter
1/2 * 3 = 3/2
Now add the thickness for the total radius
3/2 + 3/8 = 12/8 + 3/8 = 15/8
Find volume of the lead where volume = pi r^2 h
Lead vol (V) = Overall volume - inner volume
Lead Vol = pi(15/8)^2(240) - pi(3/2)^2(240)
Lead Vol = 240pi(225/64 - 9/4)
9/4 = 144/64
Lead Vol = 240pi(225/64 - 144/64)
Lead Vol = 240pi(81/64)
[B]Lead Vol = 303.75pi[/B]

A mug has 3 inch diameter and is 3.5 inches tall how much water can it hold

A mug has 3 inch diameter and is 3.5 inches tall how much water can it hold
A mug is a cylinder. If the diameter is 3, then the radius is 3/2 = 1.5.
Using our cylinder volume calculator, we get:
[B]V = 7.875pi or 24.74 cubic inches[/B]

A rectangular fish tank has a base that is 8 inches by 7 inches. How much water will it take to a de

A rectangular fish tank has a base that is 8 inches by 7 inches. How much water will it take to a depth of 5 inches
The volume (V) or a rectangular solid is:
V = lwh
Using l = 8, w = 7, and h = 5, we have:
V = 8(7)(5)
V = [B]280 cubic inches[/B]

A rectangular prism has a width of x feet, a length of y feet, and a height of h feet. Express its v

A rectangular prism has a width of [I]x[/I] feet, a length of [I]y[/I] feet, and a height of [I]h[/I] feet. Express its volume in square inches.
V = width * length * height
V = xyh
12 inches to a foot, so:
In cubic feet, we have 12 * 12 * 12 = 1728 cubic inches
V [B]= 1728xyh[/B]

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every n minut

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every [I]n[/I] minutes. How many minutes until the spacecraft has no air?
800 cubic feet / .4 cubic feet every n minutes = 2000 (n minute parts)
Total time = [B]2000n[/B]

A spherical water tank holds 11,500ft^3 of water. What is the diameter?

A spherical water tank holds 11,500ft^3 of water. What is the diameter?
The tank holding amount is volume. And the volume of a sphere is:
V = (4pir^3)/3
We know that radius is 1/2 of diameter:
r =d/2
So we rewrite our volume function:
V = 4/3(pi(d/2)^3)
We're given V = 11,500 so we have:
4/3(pi(d/2)^3) = 11500
Multiply each side by 3/4
4/3(3/4)(pi(d/2)^3) = 11,500*3/4
Simplify:
pi(d/2)^3 = 8625
Since pi = 3.1415926359, we divide each side by pi:
(d/2)^3 = 8625/3.1415926359
(d/2)^3 = 2745.42
Take the cube root of each side:
d/2 = 14.0224
Multiply through by 2:
[B]d = 28.005[/B]

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack
The lumber stack is a rectangular solid. The Volume V is found from the length (l), width (w), and height (h) by:
V = lwh
Plugging in our given values, we get:
V = 2 * 8 * 5
V = [B]80 cubic feet[/B]

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box?
The volume of the box is l x w x h. We're given l and w = 4. So we want height:
56 = 4 x 4 x h
16h = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get:
h = [B]3.5[/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty
Assumptions and givens:
[LIST]
[*]Let the number of seconds be s.
[*]An empty tank means 0 liters of water.
[*]Leaks mean we subtract from the starting volume.
[/LIST]
We have the following relation:
800 - 12s = 0
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get:
s = 66.67 seconds

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 c

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 cubic inches. The picture shows the cereal boxes she has collected so far. A large delivery box holds three times as many boxes as Anna collected.
About what is the volume of the delivery box?
The picture has 12 cereal boxes. Since the delivery box holds three times as many cereal boxes as Anna collected, the delivery box holds 12 * 3 = 36 cereal boxes.
With each cereal box having a volume of 324 cubic inches, we have the total volume as:
V = 324 cubic inches * 36 cereal boxes
V = [B]11,664 cubic inches[/B]

Assume that a balloon is spherical shaped. If you have a balloon with the radius of 3, what’s the vo

Assume that a balloon is spherical shaped. If you have a balloon with the radius of 3, what’s the volume?
Using our [URL='https://www.mathcelebrity.com/sphere.php?num=3&pl=Radius']sphere calculator[/URL], we get Volume (V):
V = [B]36pi or 113.0973[/B]

Combined Gas Law

Free Combined Gas Law Calculator - This will solve for any of the 6 items in the Combined Gas Law using pressure, volume (Capacity), and temperature.

(P_{1} x V_{1})/T1 = (P_{2} x V_{2})/T2

(P

Cones

Free Cones Calculator - Calculates and solves for Radius, height, Volume (Capacity), Lateral Area, and Surface Area of a Cone.

Cube

Free Cube Calculator - Solves for Volume (Capacity), Lateral Area,Surface Area, and the value of a side for a cube.

Cuboid

Free Cuboid Calculator - Calculates the volume, surface area, diagonals, and space diagonal for a cuboid

Cylinders

Free Cylinders Calculator - Calculates and solves for Radius, Diameter, Volume (Capacity), Lateral Area, and Surface Area of a Cylinder.

Density

Free Density Calculator - Solves for any of the 3 items in the Density Formula, Density (D), Mass (M), and Volume (V) (Capacity), with 2 given items.

Don wants to bring some sand home from his vacation at the beach. He has a box that is 3 inches wide

Don wants to bring some sand home from his vacation at the beach. He has a box that is 3 inches wide, 4 inches long, and 2 inches tall. How much sand can he fit in the box?
We want the volume. The volume of a rectangular solid is found with the formula:
V = lwh
V = 4 * 3 * 2
V = [B]24 cubic inches[/B]

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete,

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete, how many bricks did they make?
Volume of a brick (V) is:
V = l * w * h
Plugging in our brick measurements, we get:
V = 14 * 8 * 5
V = 560
Calculate number of bricks:
Number of Bricks = Total Volume / Volume of one Brick
Number of Bricks = 16,800/560
Number of Bricks =[B]30[/B]

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height is 3 feet.
The shape is a rectangular solid. The Volume (V) is shown below:
V = lwh
V = 6 * 4 * 3
V = [B]72 cubic feet[/B]

Hemisphere

Free Hemisphere Calculator - Calculates the base circumference, volume, curved surface area, base surface area, total surface area of a hemisphere with radius r

High and Low Method

Free High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula

High-Low Method

Free High-Low Method Calculator - Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method

How many cubic inches are in a cubic foot?

How many cubic inches are in a cubic foot?
Volume of a cube with 12 inch (1 foot sides) = 12 * 12 * 12 = [B]1728 cubic inches[/B]

How much sand is needed to fill a pit that measures 8 meters deep, 10 meters wide, and 15 meters lon

How much sand is needed to fill a pit that measures 8 meters deep, 10 meters wide, and 15 meters long? Explain your answer.
The pit is a rectangular solid. The volume is:
V = l * w * h
V = 15 * 10 * 8
V = [B]1,200 cubic meters[/B]

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long wil

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long will it take to fill up the pool using all 3 hoses?
Let V be the pool's Volume. Each hour, the hoses fill up this much of the pool:
[LIST]
[*]Hose A, V/6 of the pool
[*]Hose B, V/3 of the pool
[*]Hose C, V/2 of the pool
[/LIST]
Effective fill rate is:
V/6 + V/3 + V/2
6V/36 + 12V/36 + 18V/36
36V/36 which is volume units per hour
Let t = units / rate
t = 1 hour, so we have:
t = units / rate
t = V (volume units) / V (volume units / hour)
t = [B]1 hour[/B]

If V is the volume of a cube whose side is s, express s in terms of V:

If V is the volume of a cube whose side is s, express s in terms of V:
We know the Volume (V) of a cube with side length s is:
V = s^3
Take the cube root of each side:
V^1/3 = (s^3)^1/3
s = [B]V^1/3[/B]

Jethro wants a swimming pool in his backyard, so he digs a rectangular hole with dimensions 40 feet

Jethro wants a swimming pool in his backyard, so he digs a rectangular hole with dimensions 40 feet long, 20 feet wide, and 5 feet deep. How many cubic feet of water will the pool hold?
This is a rectangular solid. The volume is l x w x h:
V = 40 x 20 x 5
V = [B]4,000 cubic feet[/B]

Math Problem Solving (Help Please)

A box in the shape of a rectangular prism is used in a movie scene. The base of the box measures 6 feet by 5 feet. The box has a volume of 195 cubic feet. The director hires an actor who is 6 feet 4 inches tall. Can the actor stand up straight in the box?
Also I do need to show my work so please write down the work to solve this. Thanks!

Math Problem Solving (Help Please)

Volume of rectangular prism is:
V = lwh
Plugging in the numbers you gave:
195 = (6)(5)h
195 = 30h
Divide each side by 30
h = 6.5
6.5 feet is 6 feet, 6 inches. This is 2 inches more than your actor, so [B]yes[/B], he will fit in the box standing up.

Math Written Assignment

The truck bed is 80 inches long, 69 inches wide, and 20 inches tall. So the total volume the truck can carry is:
80 x 69 x 20 = 110,400 cubic inches can be carried each time.
Find out how many gallons in a full tank for the 2003 Ford F150.
Then you calculate the amount of miles you can drive on a full trip.

Math Written Assignment

Do you have a picture? I need the measurements to calculate volume.

Math Written Assignment

[QUOTE="math_celebrity, post: 1040, member: 1"]Do you have a picture? I need the measurements to calculate volume.[/QUOTE]
Yes here u go

Please help me!! I don't understand!

Figure 1, we have a cone, cylinder, and cube. Let's get the volume of each
Cone volume = pir^2h/3
radius = s/2
h = s
Cone Volume = pi(s/2)^2(s)/3
Cone Volume = pis^3/12
Volume of cube = s^3
Volume of cylinder = pir^2h
Volume of cylinder = pi(s/2)^2s
Volume of cylinder = pis^3/2
But Figure 2 has no sizes? For sides, height, etc. So I cannot answer the question until I have that.

Pool Volume

Free Pool Volume Calculator - Given a round shaped pool, this calculates the volume (Capacity) in gallons of the pool when filled with water

Pressure Law

Free Pressure Law Calculator - This will solve for any of the 4 items in the Pressure Law equation, also known as Gay-Lussacs Law assuming constant volume

P1 ÷ T1 = P2 ÷ T2

P1 ÷ T1 = P2 ÷ T2

Pyramids

Free Pyramids Calculator - Solves for Volume (Capacity), Surface Area, height, or radius of a Pyramid.

Rectangular Solid

Free Rectangular Solid Calculator - Solves for Volume (Capacity) of rectangular solid

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Spheres

Free Spheres Calculator - Calculates and solves for Volume (Capacity), Surface Area, and Radius of a Sphere.

the book is 11 inches long, 11 inches wide, and 2 inches thick. find the volume of the book

the book is 11 inches long, 11 inches wide, and 2 inches thick. find the volume of the book
The book is a rectangular solid, so our Volume (V) is:
V = l * w * h
V = 11 * 11 * 2
V = [B]242 cubic inches[/B]

The volume of a cube is 64. Its surface area is

Volume of a cube is s^3 where s is the length of one side.
V = 64
s^3 = 64
Take the cube root of each side:
s = 4 since 4^3 = 64
Surface Area of a cube is 6s^2. With s = 4, we have:
SA = 6(4)^2
SA =6(16)
SA =[B] 96
[MEDIA=youtube]nDSA2NDO9to[/MEDIA][/B]

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a 4 inch diameter. What is the volume of the space remaining in the cylinder?
Volume of each ball is 4/3 πr^3
V = 4/3 * 3.1415 * 2^3
V = 1.33 * 3.1415 * 8 = 33.41 cubic inches
The volume of 3 balls is:
V = 3(33.41)
V = 100.23
Volume of the cylinder is area of circle times height:
V = 3.14 * 2 * 2 * 1 = 150.72
Volume of remaining space is:
V = Volume of cylinder - Volume of 3 balls
V = 150.72 - 100.23
V = [B]50.49[/B]

Torus

Free Torus Calculator - Calculates the volume of a torus and surface area of a torus given major radius and minor radius.

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Water flows from tank A to tank B at the rate of 2 litres per minute.

Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute.
After how many minutes are there equal volumes of water in the 2 tanks?
Write an equation and solve it.

Water flows from tank A to tank B at the rate of 2 litres per minute.

[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute.
After how many minutes are there equal volumes of water in the 2 tanks?
Write an equation and solve it.[/QUOTE]
Tank A: V = 200 - 2x
Tank B: V = 100 - 0.5x
Where x is the number of minutes passed.
Set them equal to each other
200 - 2x = 100 - 0.5x
Subtract 100 from each side:
100 - 2x = -0.5x
Add 2x to each side:
1.5x = 100
Divide each side of the equation by x:
x = 66.66666667

What is the formula for the volume of a cylinder?

What is the formula for the volume of a cylinder?
The Volume (V) of a cylinder with radius (r) and height (h) is:
[B]V = πr^2h[/B]