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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.

Answer 1

To find the volume of a cone, we 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.

In this case, we have:

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

Now we can plug these values into the formula:

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

Calculating \( (9)^2 \):

\[ (9)^2 = 81 \]

Now substituting that back into the volume formula:

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

Calculating \( 81 \times 5 \):

\[ 81 \times 5 = 405 \]

Now substituting that into the volume formula:

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

Calculating \( 3.14 \times 405 \):

\[ 3.14 \times 405 = 1277.7 \]

Now taking one third of that:

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

Thus, the volume of the cone is approximately \( \boxed{425.9} \) cubic inches.