42 results

radius - Distance from the center of a circle to the edge

Formula: C/2π

(3,3) radius of 4

(3,3) radius of 4
We have a circle with center (3,3) with a radius of 4.
[URL='https://www.mathcelebrity.com/eqcircle.php?h=3&k=3&r=4&calc=1&d1=-1&d2=2&d3=3&d4=2&ceq=%28x+%2B+3%29%5E2+%2B+%28y+-+2%29%5E2+%3D+16&pl=Calculate']Use our circle equation calculator to get the general form and standard form.[/URL]

A circle has a center at (6, 2) and passes through (9, 6)

A circle has a center at (6, 2) and passes through (9, 6)
The radius (r) is found by [URL='https://www.mathcelebrity.com/slope.php?xone=6&yone=2&slope=+2%2F5&xtwo=9&ytwo=6&pl=You+entered+2+points']using the distance formula[/URL] to get:
r = 5
And the equation of the circle is found by using the center (h, k) and radius r as:
(x - h)^2 + (y - k)^2 = r^2
(x - 6)^2 + (y - 2)^2 = 5^2
[B](x - 6)^2 + (y - 2)^2 = 25[/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 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 painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint s

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint should she use to paint the sculpture
Area of a circle (A) is:
A = πr²
Substituting r = 5 into this formula, we get:
A = π * 5²
A = [B]25π[/B]

A penny has a diameter of 19 millimeters. What is the radius of the penny.

A penny has a diameter of 19 millimeters. What is the radius of the penny.
D = 2r
To solve for r, we divide each side by 2:
r = D/2
Plugging in D = 19, we get:
r = [B]19/2 or 9.5[/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 tractor tire has a radius of 24 inches. If the tire rotates one time around, about how many inches

A tractor tire has a radius of 24 inches. If the tire rotates one time around, about how many inches of ground will it cover? Use 3.14 for pi.
A tractor tire is a circle. We want the circumference, which is the distance around the tire.
C = 2pir
C = 2(3.1415)24
[B]C ~ 150.8[/B]

Annulus

Free Annulus Calculator - Calculates the area of an annulus and the equation of the annulus using the radius of the large and small concentric circles.

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]

can someone help me with how to work out this word problem?

Consider a paper cone, pointing down, with the height 6 cm and the radius 3 cm; there is currently 9/4 (pie) cubic cm of water in the cone, and the cone is leaking at a rate of 2 cubic centimeters of water per second. How fast is the water level changing, in cm per second?

center (3, -2), radius = 4

center (3, -2), radius = 4
To see the general form or standard form, you can check out this link:
[URL='http://Circle Equations']https://www.mathcelebrity.com/eqcircle.php?h=3&k=-2&r=4&d1=1&d2=1&d3=2&d4=4&calc=1&ceq=&pl=Calculate[/URL]

Centripetal Acceleration

Free Centripetal Acceleration Calculator - Solves for any of the 3 items in the centripetal acceleration formula, centripetal acceleration, rotational speed, and radius.

Chord

Free Chord Calculator - Solves for any of the 3 items in the Chord of a Circle equation, Chord Length (c), Radius (r), and center to chord midpoint (t).

Circle Equation

Free Circle Equation Calculator - This calculates the standard equation of a circle and general equation of a circle from the following given items:

* A center (h,k) and a radius r

* A diameter A(a_{1},a_{2}) and B(b_{1},b_{2})

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

* A center (h,k) and a radius r

* A diameter A(a

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

Circles

Free Circles Calculator - Calculates and solves for Radius, Diameter, Circumference, and Area of a Circle.

Cones

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

Cylinders

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

Equilateral Triangle

Free Equilateral Triangle Calculator - Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in the center and when she had painted a circle with a 5-foot diameter, she used one quart of paint. How many more quarts of paint must Fantasia buy to finish her room?
The area formula for a circle is:
Area = pir^2
Area of full room
Radius = D/2
Radius = 25/2
Radius = 12.5
Area = 3.1415 * 12.5 * 12.5
Area = 490.625
Area of 5-foot diameter circle
Radius = D/2
Radius = 5/2
Radius = 2.5
Area = 3.1415 * 2.5 * 2.5
Area = 19.625
So 1 quart of paint covers 19.625 square feet
Area of unpainted room = Area of Room - Area of 5-foot diameter circle
Area of unpainted room = 490.625 - 19.625
Area of unpainted room = 471
Calculate quarts of paint needed:
Quarts of paint needed = Area of unpainted Room / square feet per quart of paint
Quarts of paint needed = 471/19.625
Quarts of paint needed = [B]24 quarts[/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

if my diameter is 19 inches, what is my radius?

if my diameter is 19 inches, what is my radius?
Radius = Diameter/2
Radius = [B]19/2[/B]

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet and each table top has a diameter of 4 feet. If the price of a piece of plywood is $40, what is the value of the plywood that is wasted after the table tops are cut?
Area of the plywood = 4 * 8 = 32 square feet
[U]Calculate area of 1 round top[/U]
Diameter = 2
Radius = Diameter/2 = 4/2 = 2
Area of each round top = pir^2
Area of each round top = 3.14 * 2 * 2
Area of each round top = 12.56 square feet
[U]Calculate area of 2 round tops[/U]
Area of 2 round tops = 12.56 + 12.56
Area of 2 round tops = 25.12 sq feet
[U]Calculate wasted area:[/U]
Wasted area = area of the plywood - area of 2 round tops
Wasted area = 32 - 25.12
Wasted area = 6.88 sq feet
[U]Calculate cost per square foot of plywood:[/U]
Cost per sq foot of plywood = Price per plywood / area of the plywood
Cost per sq foot of plywood = 40/32
Cost per sq foot of plywood = $1.25
[U]Calculate the value of the plywood:[/U]
Value of the plywood = Wasted Area sq foot * Cost per sq foot of plywood
Value of the plywood = 6.88 * 1.25
Value of the plywood = [B]$8.60[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece?
A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches.
Area of a circle is pi(r^2). With r = 7, we have:
A =7^2(pi)
A = 49pi
Area of a slice of pizza is the area of the full pizza divided by 8
A(Slice) = [B]49pi/8[/B]

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.

Polygons

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Pyramids

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

Rectangles and Parallelograms

Free Rectangles and Parallelograms Calculator - Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Right Triangles

Free Right Triangles Calculator - This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Spheres

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

The button on Alice's shirt has a diameter of 8 millimeters. What is the button's radius?

The button on Alice's shirt has a diameter of 8 millimeters. What is the button's radius?
Radius = Diameter / 2
Radius = 8/2
Radius = [B]4[/B]

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.
The moon is a sphere. So our Surface Area formula is:
S =4pir^2
If diameter is 2,159, then radius is 2,159/2 = 1079.5. Plug this into the Surface Area of a sphere formula:
S = 4 * pi * 1079.5^2
S = 4 * pi *1165320.25
S = 4661281 pi
S = [B]14,643,846.15 square miles[/B]

The square of the radius r

The square of the radius r
The square means you raise r to the power of 2:
[B]r^2[/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.

What is the formula for the area of a circle?

What is the formula for the area of a circle?
Given a radius r, we have Area (A) of:
[B]A = πr^2[/B]

What is the formula for the circumference of a circle?

What is the formula for the circumference of a circle?
Given radius r and diameter d, the circumference C is:
[B]C = 2πr or πd[/B]

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]

When a circle's radius triples, what happens to its area?

When a circle's radius triples, what happens to its area?
A = πr^2
When r = 3r, then we have:
a = π(3r)^2
A = 9(πr^2)
This means Area increases by [B]9x
[MEDIA=youtube]j5aqShSh4uE[/MEDIA][/B]

When the circumference of a circle is increased from 10 pi inches to 15 pi inches, by how many inche

When the circumference of a circle is increased from 10 pi inches to 15 pi inches, by how many inches is the radius increased?
C = 2pir
Smaller circle:
2pir = 10pi
Divide each side by 2pi:
r = 5
Larger circle:
2pir = 15pi
Divide each side by 2pi:
r = 7.5
Difference = 7.5 - 5 = [B]2.5 or 2&1/2
[MEDIA=youtube]HvMNNffcv78[/MEDIA][/B]