Question

How do I calculate the surface area of a cylinder with a height of 10 cm and a radius of 4 cm?

Answer 1

To calculate the surface area of a cylinder, you can use the following formula:

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant (approximately 3.14159).

Given:
- \( r = 4 \) cm
- \( h = 10 \) cm

Now, substituting the values into the formula:

\[
\text{Surface Area} = 2\pi (4)(10 + 4)
\]

First, calculate \( (10 + 4) \):

\[
10 + 4 = 14
\]

Next, substitute this back into the formula:

\[
\text{Surface Area} = 2\pi (4)(14)
\]

Now multiply \( 4 \) and \( 14 \):

\[
4 \times 14 = 56
\]

Now substitute that value into the equation:

\[
\text{Surface Area} = 2\pi (56)
\]

Now calculate \( 2 \times 56 \):

\[
2 \times 56 = 112
\]

Finally, the surface area becomes:

\[
\text{Surface Area} = 112\pi
\]

If you want a numerical approximation, using \( \pi \approx 3.14159 \):

\[
\text{Surface Area} \approx 112 \times 3.14159 \approx 351.86 \text{ cm}^2
\]

So, the surface area of the cylinder is approximately \( 351.86 \) cm².