Question

A cylindrical cup is 8 centimeters in height. When filled to the very top, it holds 480 cubic centimeters of water. What is the radius of the cup, rounded to the nearest tenth? Use 3.14 for
π
. Explain or show your reasoning.

Answer 1

To find the radius of the cylindrical cup, 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 of the base,
- \( h \) is the height of the cylinder.

From the problem, we have:
- \( V = 480 \) cubic centimeters,
- \( h = 8 \) centimeters,
- \( \pi \approx 3.14 \).

We can rearrange the formula to solve for the radius \( r \):

\[
r^2 = \frac{V}{\pi h}
\]

Substituting in the values we have:

\[
r^2 = \frac{480}{3.14 \times 8}
\]

Calculating the denominator:

\[
3.14 \times 8 = 25.12
\]

Now substitute this value back into the equation for \( r^2 \):

\[
r^2 = \frac{480}{25.12}
\]

Calculating this gives:

\[
r^2 \approx 19.04
\]

Next, we take the square root of \( r^2 \) to find \( r \):

\[
r \approx \sqrt{19.04} \approx 4.36
\]

Finally, rounding to the nearest tenth:

\[
r \approx 4.4
\]

Therefore, the radius of the cup is approximately **4.4 centimeters**.