Question

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a model of a volcano has a height of 12 in, and a diameter of 12 in.
what is the approximate volume of the model?
use 3.14 to approximate pi, and express your final answer as a decimal.
enter your answer as a decimal in the box.
□ in³

Explanation:

Step1: Determine the radius

The diameter is 12 in, so the radius \( r=\frac{12}{2}=6 \) in.

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^{2}h \), where \( h \) is the height.

Step3: Substitute the values

We know \( \pi\approx3.14 \), \( r = 6 \) in, and \( h = 12 \) in. Substituting these into the formula:
\( V=\frac{1}{3}\times3.14\times6^{2}\times12 \)
First, calculate \( 6^{2}=36 \). Then:
\( V=\frac{1}{3}\times3.14\times36\times12 \)
\( \frac{1}{3}\times36 = 12 \), so:
\( V = 3.14\times12\times12 \)
\( 12\times12 = 144 \), then:
\( V=3.14\times144 \)
\( 3.14\times144 = 452.16 \)

Answer:

452.16