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
