Question

What is the total area of the two bases of a cylinder with diameters 2cm and 15cm?

Answer 1

To find the total area of the two bases of a cylinder, we first need to calculate the area of one base and then multiply that by 2, as there are two bases.

The area \( A \) of a circle (which is the shape of the base of a cylinder) is given by the formula:

\[
A = \pi r^2
\]

where \( r \) is the radius of the circle.

1. **For the base with a diameter of 2 cm:**
- The radius \( r_1 \) is half of the diameter:
\[
r_1 = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm}
\]
- Now, we calculate the area \( A_1 \) of this base:
\[
A_1 = \pi (1 \, \text{cm})^2 = \pi \cdot 1 = \pi \, \text{cm}^2
\]

2. **For the base with a diameter of 15 cm:**
- The radius \( r_2 \) is:
\[
r_2 = \frac{15 \, \text{cm}}{2} = 7.5 \, \text{cm}
\]
- Now, we calculate the area \( A_2 \) of this base:
\[
A_2 = \pi (7.5 \, \text{cm})^2 = \pi \cdot 56.25 = 56.25\pi \, \text{cm}^2
\]

3. **Total area of the two bases:**
- We add the areas of the two bases together:
\[
A_{\text{total}} = A_1 + A_2 = \pi + 56.25\pi = (1 + 56.25)\pi = 57.25\pi \, \text{cm}^2
\]

Thus, the total area of the two bases of the cylinder is

\[
\boxed{57.25\pi} \, \text{cm}^2
\]