Question

What is the volume of a cylindrical bucket that is 35 cm tall and has a base with a diameter of 21 cm? Use Pi = StartFraction 22 Over 7 EndFraction and round your answer to the nearest tenth of a cubic centimeter.

cm3

Answer 1

To calculate the volume \( V \) of a cylindrical bucket, we can use the formula:

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

Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately \( \frac{22}{7} \).

Given:
- The height \( h = 35 \) cm,
- The diameter of the base is 21 cm, so the radius \( r \) is half of that:

\[
r = \frac{21}{2} = 10.5 \, \text{cm}
\]

Now we can substitute the values into the volume formula:

\[
V = \frac{22}{7} \times (10.5)^2 \times 35
\]

First, calculate \( (10.5)^2 \):

\[
(10.5)^2 = 110.25
\]

Next, substitute into the volume equation:

\[
V = \frac{22}{7} \times 110.25 \times 35
\]

Now compute \( 110.25 \times 35 \):

\[
110.25 \times 35 = 3868.75
\]

Now substitute this back into the volume formula:

\[
V = \frac{22}{7} \times 3868.75
\]

Calculating \( \frac{22}{7} \times 3868.75 \):

\[
V = 22 \times 3868.75 \div 7
\]

Calculate \( 22 \times 3868.75 \):

\[
22 \times 3868.75 = 85212.5
\]

Now divide by 7:

\[
V = \frac{85212.5}{7} \approx 12173.214285714287
\]

Now we round this to the nearest tenth:

\[
V \approx 12173.2 \, \text{cm}^3
\]

Thus, the volume of the cylindrical bucket is approximately:

\[
\boxed{12173.2} \, \text{cm}^3
\]