The radius and height of a cylinder are in the ratio 7:2. If the volume of the cylinder is 8316 cubic centimeters find the total surface area of the cylinder

Answer: the total surface area of the cylinder is 3572 cm²

Step-by-step explanation:

If the radius and height of a cylinder are in the ratio 7:2, it means that

r/h = 7/2 = 3.5

r = 3.5h

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

Volume = 8316

Height = h

Radius = 3.5h

Therefore,

8316 = 3.14 * (3.5h) ² * h

8316 = 38.465h³

h³ = 8316/38.465 = 216.197

Taking cube root of both sides of the equation, it becomes

h = 6.009

r = 3.5 * 6.009

r = 21.0315 cm

The formula for determining the total surface area of a cylinder is expressed as

2πr² + 2πrh

Total surface area = (2 * 3.14 * 21.0315²) + (2 * 3.14 * 21.0315 * 6.009)

= 2778 + 794

= 3572 cm²