Question

what is the total surface area of a cylinder with a height of 15 and radius of 4, round to the nearest tenth

Answer 1

To find the total surface area of a cylinder, you can use the formula:

\[
\text{Total Surface Area} = 2\pi r(h + r)
\]

where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:
- Height \( h = 15 \)
- Radius \( r = 4 \)

Substituting the values into the formula:

\[
\text{Total Surface Area} = 2\pi (4)(15 + 4)
\]

Calculating \( (15 + 4) \):

\[
15 + 4 = 19
\]

Now, substituting back into the formula:

\[
\text{Total Surface Area} = 2\pi (4)(19)
\]
\[
= 8\pi (19)
\]
\[
= 152\pi
\]

Now to get an approximate numerical value, use \( \pi \approx 3.14 \):

\[
152\pi \approx 152 \times 3.14 \approx 476.48
\]

Rounding to the nearest tenth:

\[
\text{Total Surface Area} \approx 476.5
\]

Thus, the total surface area of the cylinder is approximately **476.5 square units**.