Question

a planter is attached to a post in a garden. the planter is in the shape of half a cone. what is the volume of soil that will fit inside the planter, to the nearest cubic centimeter? (use 3.14 to approximate π) cm³

Explanation:

Step1: Find the radius of the cone

The diameter \( d = 24 \) cm, so the radius \( r=\frac{d}{2}=\frac{24}{2} = 12 \) cm.

Step2: Recall the volume formula for a full cone

The volume of a full cone is \( V_{full}=\frac{1}{3}\pi r^{2}h \).

Step3: Calculate the volume of half - cone

Since the planter is half a cone, its volume \( V=\frac{1}{2}\times\frac{1}{3}\pi r^{2}h=\frac{1}{6}\pi r^{2}h \).
Substitute \( r = 12 \) cm, \( h = 36 \) cm and \( \pi=3.14 \) into the formula:
\( V=\frac{1}{6}\times3.14\times12^{2}\times36 \)
First, calculate \( 12^{2}=144 \).
Then, \( \frac{1}{6}\times3.14\times144\times36 \)
\( \frac{1}{6}\times36 = 6 \), so the formula becomes \( 3.14\times144\times6 \)
\( 3.14\times144 = 452.16 \)
\( 452.16\times6=2712.96\approx2713 \)

Answer:

\( 2713 \)