Question

Lake City uses a cone-shaped building to store the salt they spread on their roads during winter. Each storage building has a radius of 39 feet and a height of 49 feet.

Using 3.14 for , approximately how much salt can each storage building hold?
A.
234,021.06 cubic feet
B.
78,007.02 cubic feet
C.
6,000.54 cubic feet
D.
98,008.82 cubic feet

Answer 1

To find the volume of the cone-shaped storage building, you 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,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.

Given:
- \( r = 39 \) feet,
- \( h = 49 \) feet,
- \( \pi \approx 3.14 \).

Now, substituting the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (39)^2 \times 49
\]

Calculating \( (39)^2 \):

\[
39^2 = 1521
\]

Now, substituting this into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 1521 \times 49
\]

Now, first calculate \( 1521 \times 49 \):

\[
1521 \times 49 = 74429
\]

Now substitute this back:

\[
V = \frac{1}{3} \times 3.14 \times 74429
\]

Calculating \( 3.14 \times 74429 \):

\[
3.14 \times 74429 \approx 233,185.06
\]

Now, divide by 3 to find the volume:

\[
V = \frac{233,185.06}{3} \approx 77,728.69
\]

Since this is how much salt each storage building can hold, rounding to two decimal places, you find that the storage volume is approximately \( 78,007.02 \) cubic feet.

Thus, the answer is:

**B. 78,007.02 cubic feet**.