Question

Find the lateral area of a cylinder with a radius of 2.5 meters and a height of 7 meters

Answer 1

The lateral area \( A \) of a cylinder can be calculated using the formula:

\[
A = 2\pi rh
\]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given that the radius \( r = 2.5 \) meters and the height \( h = 7 \) meters, we can substitute these values into the formula:

\[
A = 2\pi (2.5)(7)
\]

First, calculate \( 2.5 \times 7 \):

\[
2.5 \times 7 = 17.5
\]

Now plug this back into the formula:

\[
A = 2\pi (17.5)
\]

Calculating \( 2 \times 17.5 \):

\[
2 \times 17.5 = 35
\]

So, we have:

\[
A = 35\pi
\]

Now, to find the approximate value, we can use \( \pi \approx 3.14 \):

\[
A \approx 35 \times 3.14 \approx 109.9
\]

Thus, the lateral area of the cylinder is approximately:

\[
A \approx 109.9 \text{ square meters}
\]

If you want the exact answer, it is:

\[
A = 35\pi \text{ square meters}
\]

or about \( 109.9 \) square meters.