Question

A birthday cake is being made using a cylindrical baking pan. The radius of the pan is 4 inches, and the height is 5 inches. Which formula represents the correct way to calculate the volume of the cake?
V = (4) (5)
V = pi (4) (5)
V = pi (5) squared (4)
V = pi (4) squared (5)
Answer
A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.
The sphere has a diameter of 8 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed.
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
The diameter’s length is one-half the length of the radius.
Answer
What is the height of a cylinder with a volume of 384 pi cubic inches and a radius of 8 inches? Round to the nearest tenth of an inch.
Answer
What number can be used to complete the volume statement for the cone?

A cone with height 4 meters and diameter 3 meters.

Volume =
Pi meters cubed
Answer
A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to the nearest tenth. Use 3.14 for Pi.

cubic inches
Answer
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

A sphere with height h and radius r. A cylinder with height h and radius r.

Which equation gives the volume of the sphere?
V = two-thirds (27 pi)
V = four-thirds (27)
V = two-thirds (27)
V = four-third (27 pi)
Answer
James calculated the height of a cylinder that has a volume of 324 pi cubic inches and a radius of 12 inches. His work is shown below.

V = B h
Step 1: 324 pi = pi 12 squared h
Step 2: 324 pi = 24 pi h
Step 3: StartFraction 324 pi over 24 pi EndFraction = StartFraction 24 pi over 24 pi EndFraction h
Step 4: h = 13.5 pi inches

What is the first error that James made when calculating the height of the cylinder?
In step 1, he substituted into the volume formula incorrectly.
In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24.
In step 4, the Pi should have canceled, making the correct answer 13.5 cm.
James calculated the height of the cylinder correctly.
Answer
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.

A sphere with height h and radius r. A cylinder with height h and radius r.

Her work is shown below.

V = four-thirds (8) cubed. V = four-thirds (512). V = StartFraction 2,048 Over 3 EndFraction meters cubed.

What is Yolanda’s error?
Yolanda should have found the volume by multiplying 8 by Two-thirds.
Yolanda should have found the volume by multiplying 8 by Four-thirds.
Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.
Yolanda should have found the volume with the formula V = two-thirds (8) cubed.
Answer
Sondra has a conical bird feeder with a circular top. The volume of the bird feeder is 153.86 cubic inches. The height of the feeder is 12 inches. What is radius of the top? Use 3.14 for Pi. Round the answer to the nearest tenth.
3.5 in.
7.0 in.
12.3 in.
49.0 in.
Answer
An icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 27 mm. In cubic millimeters, how much frozen water is in the icicle? Use 3.14 for Pi. Round your answer to the nearest hundredth.

Answer
Vaughn is calculating the volume of the cylinder below using the following work.

A cylinder with height of 24 centimeters and diameter of 5 centimeters.

mc016-2.jpg

What was Vaughn’s first error?
He confused the height and the diameter.
He squared 12 instead of 24.
He applied the exponent before multiplying 12 and 5.
He used the wrong units in his final answer.
Answer
An icicle is in the shape of an inverted cone with a diameter of 14 mm and a height of 60 mm. How much frozen water is in the icicle? Use 3.14 for Pi. Round the answer to the nearest tenth.
188.4 millimeters cubed
980.0 millimeters cubed
3,077.2 millimeters cubed
9,231.6 millimeters cubed
Answered by Bot
The correct formula to calculate the volume of the cake is V = pi (4 squared) (5)
Answered by Bot
The correct statements about the sphere are:
- The sphere has a diameter of 32 in.
- The volume of the sphere is 16,384π cubic inches.
- The radius's length is one-half the length of the diameter.
- The diameter's length is one-half the length of the radius.
Answered by Bot
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the volume is 384π cubic inches and the radius is 8 inches, we can rearrange the formula to solve for the height:

384π = π(8^2)h
384 = 64h
h = 384/64
h = 6 inches

Therefore, the height of the cylinder is 6 inches.
Answered by Bot
To calculate the volume of a cone, the formula is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the height is 4 meters and the diameter is 3 meters, we can calculate the radius by dividing the diameter by 2:

Radius = Diameter/2 = 3/2 = 1.5 meters

Now, we can substitute the values into the formula to find the volume:

V = (1/3)π(1.5^2)(4)
V = (1/3)π(2.25)(4)
V = (1/3)π(9)
V = (1/3)(9π)
V = 3π

Therefore, the volume of the cone is 3π meters cubed.
Answered by Bot
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the radius is 4 inches and the height is 15 inches, we can substitute the values into the formula to find the volume:

V = π(4^2)(15)
V = π(16)(15)
V = π(240)
V = 240π

To round to the nearest tenth, we can use the value of π as 3.14:

V = 240(3.14)
V = 753.6

Therefore, the volume of the paint can is approximately 753.6 cubic inches.
Answered by Bot
The equation that gives the volume of the sphere is V = four-thirds (27 pi).
Answered by Bot
The first error that James made when calculating the height of the cylinder is "In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24."
Answered by Bot
Yolanda's error is "Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed."
Answered by Bot
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the volume is 153.86 cubic inches and the height is 12 inches, we can rearrange the formula to solve for the radius:

153.86 = (1/3)π(r^2)(12)
3(153.86) = 12π(r^2)
461.58 = 12π(r^2)
461.58/12π = r^2
r^2 ≈ 12.139

Taking the square root of both sides to find the radius:

r ≈ √12.139
r ≈ 3.483

Rounding to the nearest tenth, the radius of the top of the bird feeder is approximately 3.5 inches.

Therefore, the correct answer is 3.5 in.
Answered by Bot
To find the volume of the icicle, we need to calculate the volume of the cone. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the diameter is 9 mm, we can calculate the radius by dividing the diameter by 2:

Radius = Diameter/2 = 9/2 = 4.5 mm

Now we can substitute the values into the formula:

V = (1/3)π(4.5^2)(27)
V ≈ 3.14(20.25)(27)
V ≈ 1696.85 mm^3

Rounding to the nearest hundredth, the frozen water in the icicle is approximately 1696.85 cubic millimeters.

Therefore, the correct answer is 1696.85 mm^3.
Answered by Bot
From the provided illustration, it appears that Vaughn's first error was that he confused the height and the diameter.
Answered by Bot
To find the volume of the icicle, we need to calculate the volume of the cone. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the diameter is 14 mm, we can calculate the radius by dividing the diameter by 2:

Radius = Diameter/2 = 14/2 = 7 mm

Now we can substitute the values into the formula:

V = (1/3)π(7^2)(60)
V ≈ (1/3)(3.14)(49)(60)
V ≈ 18,435.6 mm^3

Rounding to the nearest tenth, the frozen water in the icicle is approximately 18,435.6 cubic millimeters.

Therefore, the correct answer is 18,435.6 millimeters cubed.