Surface Area Sample Work

Answer 1

Example:

Find the surface area of a cylinder with a radius of 5 cm and a height of 10 cm.

First, calculate the lateral surface area of the cylinder:

Lateral surface area = 2πrh
= 2(3.14)(5)(10)
= 314 cm²

Next, calculate the surface area of the two circular bases:

Base area = πr²
= 3.14(5)²
= 78.5 cm²

Since there are two circular bases, the total area of both bases is:

Total base area = 2(78.5)
= 157 cm²

Finally, add the lateral surface area and the total base area to get the total surface area of the cylinder:

Total surface area = Lateral surface area + Total base area
= 314 + 157
= 471 cm²

Therefore, the surface area of the cylinder is 471 cm².