Question

A can holds 753.6 cubic centimeters of juice. The can has a diameter of 8 centimeters. What is the height of the can? Use 3.14 for π and round to the nearest centimeter.

About
cm

Answer 1

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

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

where:
- \( V \) is the volume (753.6 cm³),
- \( r \) is the radius of the base, and
- \( h \) is the height.

First, we need to calculate the radius of the base. Given that the diameter of the can is 8 cm, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ cm}
\]

Now we substitute the values into the volume formula and solve for \( h \):

\[
753.6 = 3.14 \times (4^2) \times h
\]

Calculating \( 4^2 \):

\[
4^2 = 16
\]

Substituting back in:

\[
753.6 = 3.14 \times 16 \times h
\]

Calculating \( 3.14 \times 16 \):

\[
3.14 \times 16 = 50.24
\]

Now we have:

\[
753.6 = 50.24h
\]

To find \( h \), we divide both sides by 50.24:

\[
h = \frac{753.6}{50.24}
\]

Calculating the right side:

\[
h \approx 14.99
\]

Rounding to the nearest centimeter:

\[
h \approx 15 \text{ cm}
\]

Thus, the height of the can is approximately **15 cm**.