The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area.
a) 3010.5
b) 3391.2
c) 3232.3
d) 3555.4
Sol:
Let the height be 7x and radius be 5x
According to the question,
Volume = π (5x)2 × 7x
⇒ 14836.5 = (3.14)(25×2) × 7x
⇒ 14836.5 = (3.14)(25×2) × 7x
⇒ 175×3 = 14836.5/3.14
⇒ x3 = 4725/175
⇒ x3 = 27
⇒ x = 3
Now, Radius = 5x = 5 × 3 = 15 cm
Height = 7x = 7 × 3 = 21 cm
For TSA of cylinder,
TSA = 2(3.14) × 15 × (15 + 21)
⇒ TSA = 6.28 × 15 × 36
⇒ TSA = 3391.2 cm2
∴ The TSA of the cylinder is 3391.2 cm2.
