An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.

Question

What is the volume of the cone? Use 3.14 for pi.
(1 point)

Answer 1

To calculate the volume of a cone, we 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.

Given that the base radius \( r \) is 9 inches and the perpendicular height \( h \) is 5 inches, we can substitute these values into the formula.

First, calculate \( r^2 \):

\[ r^2 = 9^2 = 81 \]

Now substitute \( r^2 \) and \( h \) into the volume formula:

\[ V = \frac{1}{3} \pi (81)(5) \]

Substituting \( \pi \) with 3.14:

\[ V = \frac{1}{3} \times 3.14 \times 81 \times 5 \]

Now calculate \( 81 \times 5 \):

\[ 81 \times 5 = 405 \]

So now the formula becomes:

\[ V = \frac{1}{3} \times 3.14 \times 405 \]

Calculate \( 3.14 \times 405 \):

\[ 3.14 \times 405 = 1277.7 \]

Now divide by 3:

\[ V = \frac{1277.7}{3} = 425.9 \]

Therefore, the volume of the cone is approximately:

\[ \boxed{425.9} \text{ cubic inches} \]