Question

Sondra has a conical bird feeder with a circular top. The volume of the bird feeder is 153.86 cubic inches. The height of the feeder is 12 inches. What is radius of the top? Use 3.14 for Pi. Round the answer to the nearest tenth.
3.5 in.
7.0 in.
12.3 in.
49.0 in.

Answer 1

To find the radius of the top of the conical bird feeder, we can use the formula for the volume of a cone:

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

Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height of the cone

Given:
- \( V = 153.86 \) cubic inches
- \( h = 12 \) inches
- Using \( \pi \approx 3.14 \)

We will rearrange the formula to solve for \( r \):

\[
153.86 = \frac{1}{3} \cdot 3.14 \cdot r^2 \cdot 12
\]

First, simplify the equation:

\[
153.86 = \frac{1}{3} \cdot 3.14 \cdot 12 \cdot r^2
\]

Calculate \( \frac{1}{3} \cdot 3.14 \cdot 12 \):

\[
\frac{1}{3} \cdot 3.14 = 1.047 \quad \text{ and then } \quad 1.047 \cdot 12 = 12.564
\]

So, the equation becomes:

\[
153.86 = 12.564 \cdot r^2
\]

Now, solve for \( r^2 \):

\[
r^2 = \frac{153.86}{12.564}
\]

Calculating that gives:

\[
r^2 \approx 12.24
\]

Now take the square root to find \( r \):

\[
r \approx \sqrt{12.24} \approx 3.49
\]

Rounding to the nearest tenth gives:

\[
r \approx 3.5 \text{ inches}
\]

Thus, the radius of the top is:

\[
\boxed{3.5 \text{ in.}}
\]