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Question

A right cone shows a base radius of 5 centimeters and a perpendicular height of 9 centimeters. A right angle is formed with the diameter and the height at the center of the circular base.
What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth. (1 point)

(blank) cubic centimeters

Answer 1

The formula for the volume \( V \) of a cone is given by:

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

where \( r \) is the radius of the base and \( h \) is the height.

Given:

• Radius \( r = 5 \) cm
• Height \( h = 9 \) cm
• Using \( \pi \approx 3.14 \)

Now, we can calculate the volume:

1. Calculate \( r^2 \): \[ r^2 = 5^2 = 25 \]

2. Substitute \( r^2 \) and \( h \) into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 25 \times 9 \]

3. Calculate \( 25 \times 9 \): \[ 25 \times 9 = 225 \]

4. Now calculate the volume: \[ V = \frac{1}{3} \times 3.14 \times 225 \]

5. Calculate \( 3.14 \times 225 \): \[ 3.14 \times 225 = 706.5 \]

6. Finally, divide by 3: \[ V = \frac{706.5}{3} = 235.5 \]

Therefore, the volume of the cone, rounded to the nearest tenth, is:

\[ \boxed{235.5} \text{ cubic centimeters} \]