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Question

A 3 D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.

Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.

(1 point)
cubic millimeters
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Answer 1

To find the volume \( V \) of a cylinder, we can use the formula:

\[ V = \pi r^2 h \]

where:

• \( r \) is the radius of the base,
• \( h \) is the height of the cylinder.

From the information given:

• The base radius \( r = 8 \) millimeters,
• The height \( h = 13 \) millimeters.

Now we can substitute these values into the formula:

\[ V = \pi (8^2) (13) \]

Calculating \( 8^2 \):

\[ 8^2 = 64 \]

Now substitute that back into the volume equation:

\[ V = \pi (64) (13) \] \[ V = 832\pi \]

Now we need to calculate \( 832\pi \). Using \( \pi \approx 3.14159 \):

\[ V \approx 832 \times 3.14159 \approx 2617.76 \]

Rounding to the nearest hundredth:

\[ V \approx 2617.76 \text{ cubic millimeters} \]

Thus, the volume of the cylinder is approximately:

\[ \boxed{2617.76} \text{ cubic millimeters} \]

Answer 2

A water bottle has a height of 16 inches and a radius of 4 inches. What is the volume, in cubic inches, of the water bottle? Use 3.14 for pi. (1 point)
cubic inches

Answer 3

To find the volume \( V \) of the water bottle (which has the shape of a cylinder), we can use the formula:

\[ V = \pi r^2 h \]

Where:

• \( r \) is the radius of the base,
• \( h \) is the height of the cylinder.

Given:

• The radius \( r = 4 \) inches,
• The height \( h = 16 \) inches.

We can substitute these values into the formula, using \( \pi \approx 3.14 \):

\[ V = 3.14 \times (4^2) \times 16 \]

First, calculate \( 4^2 \):

\[ 4^2 = 16 \]

Now substitute that back into the volume equation:

\[ V = 3.14 \times 16 \times 16 \] \[ V = 3.14 \times 256 \]

Now perform the multiplication:

\[ V \approx 3.14 \times 256 = 804.544 \]

Rounding to the nearest hundredth gives:

\[ V \approx 804.54 \text{ cubic inches} \]

Thus, the volume of the water bottle is approximately:

\[ \boxed{804.54} \text{ cubic inches} \]

Answer 4

Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches. Round your answer to the nearest hundredth. Use 3.14 for pi.(1 point)
cubic inches

Answer 5

To find the volume \( V \) of a cone, we can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( r \) is the radius of the cone,
• \( h \) is the height of the cone.

Given:

• The radius \( r = 13 \) inches,
• The height \( h = 27 \) inches.

Let's substitute these values into the formula, using \( \pi \approx 3.14 \):

\[ V = \frac{1}{3} \times 3.14 \times (13^2) \times 27 \]

First, calculate \( 13^2 \):

\[ 13^2 = 169 \]

Now substitute that back into the volume equation:

\[ V = \frac{1}{3} \times 3.14 \times 169 \times 27 \]

Now calculate \( 169 \times 27 \):

\[ 169 \times 27 = 4563 \]

Now substitute that into the volume calculation:

\[ V = \frac{1}{3} \times 3.14 \times 4563 \]

Calculating \( 3.14 \times 4563 \):

\[ 3.14 \times 4563 \approx 14349.42 \]

Now divide by 3:

\[ V = \frac{14349.42}{3} \approx 4783.140 \]

Rounding to the nearest hundredth gives:

\[ V \approx 4783.14 \text{ cubic inches} \]

Thus, the volume of the cone is approximately:

\[ \boxed{4783.14} \text{ cubic inches} \]

Answer 6

A cone-shaped container on a farm is used for storing animal feed. The container has a radius of 4 feet and a height of 12 feet. What volume of feed, in cubic feet, can the container store? Round your answer to the nearest hundredth. Use 3.14 for π
.(1 point)
cubic feet

Answer 7

To find the volume \( V \) of a cone, we can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( r \) is the radius of the cone,
• \( h \) is the height of the cone.

Given:

• The radius \( r = 4 \) feet,
• The height \( h = 12 \) feet.

Substituting these values into the volume formula (using \( \pi \approx 3.14 \)):

\[ V = \frac{1}{3} \times 3.14 \times (4^2) \times 12 \]

First, calculate \( 4^2 \):

\[ 4^2 = 16 \]

Now substitute that back into the volume equation:

\[ V = \frac{1}{3} \times 3.14 \times 16 \times 12 \]

Next, calculate \( 16 \times 12 \):

\[ 16 \times 12 = 192 \]

Now substitute that into the volume equation:

\[ V = \frac{1}{3} \times 3.14 \times 192 \]

Calculating \( 3.14 \times 192 \):

\[ 3.14 \times 192 \approx 602.88 \]

Now divide by 3:

\[ V = \frac{602.88}{3} \approx 200.96 \]

Rounding to the nearest hundredth gives:

\[ V \approx 200.96 \text{ cubic feet} \]

Thus, the volume of feed that the container can store is approximately:

\[ \boxed{200.96} \text{ cubic feet} \]

Answer 8

The diameter of a sphere(1 point)
Responses

is half the length of the radius.
is half the length of the radius.

is the distance from the center of the sphere to any point on the surface of the sphere.
is the distance from the center of the sphere to any point on the surface of the sphere.

is the longest distance on a sphere.
is the longest distance on a sphere.

does not pass through the center of the spher

Answer 9

The correct response regarding the diameter of a sphere is:

is the longest distance on a sphere.

To clarify:

• The diameter of a sphere is defined as the longest distance across the sphere, passing through the center.
• The diameter is also twice the radius, but it is not "half the length of the radius."
• It is not merely the distance from the center to the surface (which defines the radius) or a distance that does not pass through the center.

Therefore, the best answer is that the diameter is the longest distance on a sphere.

Answer 10

Cones, Cylinders, & Spheres Unit Test
10 of 1510 of 15 Items

Question
Find the surface area of a hemisphere with a radius 10m. Leave your answer in terms of pi.(1 point)
Responses

500π m2
500 pi m squared

200π m2

200 pi m squared

400π m2
400 pi m squared

300π m2
300 pi m squared
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Answer 11

To find the surface area of a hemisphere, we can use the formula:

\[ \text{Surface Area} = 2\pi r^2 + \pi r^2 \]

The first term \( 2\pi r^2 \) represents the curved surface area of the hemisphere, and the second term \( \pi r^2 \) represents the area of the circular base.

For a hemisphere with a radius \( r = 10 \) m:

1. Calculate \( r^2 \): \[ r^2 = 10^2 = 100 \]

2. Substitute \( r^2 \) into the surface area formula: \[ \text{Surface Area} = 2\pi(100) + \pi(100) = 200\pi + 100\pi = 300\pi \]

Thus, the surface area of the hemisphere is:

\[ \boxed{300\pi \text{ m}^2} \]

So the correct answer among the options provided is:

300π m².