Question

Anand models a can of ground coffee as a right cylinder. He measures its radius as one half
2
1
​
in and its volume as 4 cubic inches. Find the height of the can in inches. Round your answer to the nearest tenth if necessary.

Answer 1

To find the height of the can of ground coffee modeled as a right cylinder, 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, and
- \( h \) is the height.

From the problem, we know:
- \( V = 4 \) cubic inches,
- \( r = \frac{1}{2} \) inches.

Now, let's substitute the values into the volume formula and solve for \( h \):

1. Substitute the values of \( V \) and \( r \):

\[
4 = \pi \left(\frac{1}{2}\right)^2 h
\]

2. Calculate \( \left(\frac{1}{2}\right)^2 \):

\[
\left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]

3. Substitute this back into the equation:

\[
4 = \pi \left(\frac{1}{4}\right) h
\]

4. Multiply both sides by 4 to eliminate the fraction:

\[
16 = \pi h
\]

5. Solve for \( h \):

\[
h = \frac{16}{\pi}
\]

6. Now, calculate \( h \) using the approximation \( \pi \approx 3.14 \):

\[
h \approx \frac{16}{3.14} \approx 5.096
\]

7. Rounding to the nearest tenth:

\[
h \approx 5.1 \text{ inches}
\]

Therefore, the height of the can is approximately **5.1 inches**.