Question

Colin is purchasing a can of beans. The can is in the shape of a right circular cylinder. If the volume of the can is 31.79 inches3
, and the diameter is 3 inches, what is the height of the can? Use 3.14
for π
and round to the nearest tenth.(1 point)

Answer 1

To find the height of the can, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

Where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius,
- \( h \) is the height.

Given:
- The volume \( V = 31.79 \) inches³,
- The diameter of the can is 3 inches, which means the radius \( r \) is half of the diameter:

\[
r = \frac{3}{2} = 1.5 \text{ inches}
\]

Now we can substitute the values into the volume formula:

\[
31.79 = 3.14 \times (1.5)^2 \times h
\]

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now substituting back into the volume equation:

\[
31.79 = 3.14 \times 2.25 \times h
\]

Calculating \( 3.14 \times 2.25 \):

\[
3.14 \times 2.25 = 7.065
\]

Now we have:

\[
31.79 = 7.065 \times h
\]

To find \( h \), divide both sides by \( 7.065 \):

\[
h = \frac{31.79}{7.065}
\]

Calculating the height:

\[
h \approx 4.49
\]

Rounding to the nearest tenth, we get:

\[
h \approx 4.5 \text{ inches}
\]

Thus, the height of the can is approximately **4.5 inches**.