The total surface area of a cylinder of diameter 10 cm is 330 square centimeters. Find the height of the cylinder?

Correct option is C

Given:

Diameter of the cylinder = 10 cm.

Total surface area (TSA) of the cylinder = 330 cm².

Find the height of the cylinder.

Formula Used:

The formula for the total surface area of a cylinder:

TSA = 2πr² + 2πrh

Where:

r = radius of the base

h = height of the cylinder

Solution:

the radius of the cylinder.

Radius, r = Diameter / 2 = 10 / 2 = 5 cm.

Substitute the values into the TSA formula.

330 = 2π(5²) + 2π(5)h

330 = 2π(25) + 2π(5)h

330 = 50π + 10πh

330 = π(50 + 10h)

​$$\frac{330 }{ π} = 50 + 10h$$​​

Using π ≈ 3.14:

​$$\frac{330 }{ 3.14 }= 50 + 10h$$​​

105.1 = 50 + 10h

10h = 105.1 - 50

The height of the cylinder is approximately 5.51 cm.