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

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 2

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 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.