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)
inches

Answer 1

To find the height of a right circular cylinder (the can of beans) given the volume and diameter, we can use the formula for the volume of a cylinder:

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

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.

1. First, we need to find the radius. The diameter of the can is given as 3 inches, so the radius \( r \) is half of that:

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

2. Next, we can substitute the known values into the volume formula. We have \( V = 31.79 \) inches³ and \( r = 1.5 \) inches:

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

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

3. Now substituting this back into the equation gives:

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

Calculating \( 3.14 \times 2.25 \):

\[
3.14 \times 2.25 = 7.065
\]

4. Now we have:

\[
31.79 = 7.065 \times h
\]

5. To solve for \( h \), divide both sides by 7.065:

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

Calculating \( \frac{31.79}{7.065} \):

\[
h \approx 4.49
\]

6. Finally, rounding to the nearest tenth:

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

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