Volume of Cones Practice

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Question
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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)
cubic centimeters
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1 answer

To calculate 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 of the base,
  • \( h \) is the height of the cone,
  • \( \pi \) is approximately 3.14.

From the question:

  • The radius \( r = 5 \) cm,
  • The height \( h = 9 \) cm.

Now, substituting the values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 9 \]

Calculating step-by-step:

  1. Calculate \( (5)^2 = 25 \).
  2. Then calculate \( 3.14 \times 25 = 78.5 \).
  3. Now multiply that by the height (9): \( 78.5 \times 9 = 706.5 \).
  4. Finally, divide by 3: \( \frac{706.5}{3} = 235.5 \).

So, the volume of the cone is approximately:

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