Question

Use the image to answer the question.

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.

What is the volume of the cone? Use 3.14 for pi.

(1 point)
Responses

47.1 cubic inches
47.1 cubic inches

942 cubic inches
942 cubic inches

423.9 cubic inches
423.9 cubic inches

235.5 cubic inches
235.5 cubic inches
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Answer 1

To calculate the volume of a cone, we can use the formula:

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

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

Given:
- Base radius \( r = 9 \) inches
- Perpendicular height \( h = 5 \) inches
- Use \( \pi \approx 3.14 \)

Substituting the values into the formula:

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

Calculating \( 9^2 \):

\[
9^2 = 81
\]

Now substitute this value back into the equation:

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

Calculating \( 81 \times 5 \):

\[
81 \times 5 = 405
\]

Now substitute this value back into the volume equation:

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

Calculating \( \frac{1}{3} \times 405 \):

\[
\frac{405}{3} = 135
\]

Now substitute this back into the volume formula:

\[
V = 3.14 \times 135
\]

Calculating this gives:

\[
V = 423.9 \text{ cubic inches}
\]

Therefore, the volume of the cone is **423.9 cubic inches**.