Use the image to answer the question.

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

942 cubic inches

423.9 cubic inches

235.5 cubic inches

Answer 1

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

Given:

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

Now, plugging in the values into the formula:

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

First, calculate \( (9)^2 \):

\[ (9)^2 = 81 \]

Now we can substitute that back into the volume formula:

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

Calculate \( 81 \cdot 5 \):

\[ 81 \cdot 5 = 405 \]

Now substitute that value into the formula:

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

Next, compute \( 3.14 \cdot 405 \):

\[ 3.14 \cdot 405 = 1273.7 \]

Now, calculate \( \frac{1}{3} \cdot 1273.7 \):

\[ \frac{1}{3} \cdot 1273.7 \approx 424.5667 \]

Rounding this to one decimal place, we get approximately:

\[ V \approx 424.6 \]

Therefore, the closest answer from the options provided is:

423.9 cubic inches.