Question

Cones, Cylinders, & Spheres Unit Test 6 of 156 of 15 Items Question 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 1

Cones, Cylinders, & Spheres Unit Test 7 of 157 of 15 Items Question 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 2

To find the volume of a cylinder (which is the shape of the water bottle), you can use the formula:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.

Given:
- Height \( h = 16 \) inches
- Radius \( r = 4 \) inches

Now substitute the values into the formula:

\[
V = 3.14 \times (4)^2 \times 16
\]
\[
V = 3.14 \times 16 \times 16
\]
\[
V = 3.14 \times 256
\]
\[
V \approx 804.64
\]

So, the volume of the water bottle is approximately **804.64 cubic inches**.

Answer 3

To find the volume of a cone, you can use the formula:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius, and
- \( h \) is the height.

Given:
- Radius \( r = 13 \) inches
- Height \( h = 27 \) inches

Now substitute the values into the formula:

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

First, calculate \( r^2 \):

\[
(13)^2 = 169
\]

Now substitute this back into the equation:

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

Next, calculate \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now substitute this value into the equation:

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

Now, calculate \( 3.14 \times 4563 \):

\[
3.14 \times 4563 \approx 14361.42
\]

Now, divide by 3:

\[
V \approx \frac{14361.42}{3} \approx 4787.14
\]

So, the volume of the cone, rounded to the nearest hundredth, is approximately **4787.14 cubic inches**.