Question

Find the volume of a cylinder with a diameter of 4 mm and a height of 7.2 mm.


Choose the best answer from the options below:
A 117.6 mm 3
B 90.5 mm 3
C 361.9 mm 3
D 45.2 mm 3

Answer 1

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

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

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

1. First, we need to find the radius. The diameter of the cylinder is given as 4 mm, so the radius \( r \) is:

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

2. The height \( h \) is given as 7.2 mm.

3. Now, we can substitute the values into the volume formula:

\[
V = \pi (2 \text{ mm})^2 (7.2 \text{ mm})
\]

Calculating the squared radius:

\[
(2 \text{ mm})^2 = 4 \text{ mm}^2
\]

4. Now, substitute back into the volume formula:

\[
V = \pi (4 \text{ mm}^2) (7.2 \text{ mm}) = 28.8\pi \text{ mm}^3
\]

5. Finally, we can use the value of \( \pi \approx 3.14 \) to calculate the volume:

\[
V \approx 28.8 \times 3.14 \text{ mm}^3 \approx 90.43 \text{ mm}^3
\]

Rounding it gives us approximately \( 90.5 \text{ mm}^3 \).

The best answer from the options provided is:

**B 90.5 mm³**