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 (take π = 3.14).
Answer & explanation
Correct answer: option 1
We know that,
Volume of cylinder = πr2h
TSA of cylinder = 2πr(r + h)
Height : radius = 7 ∶ 5.
Volume = 14836.5 cm3
Let the height be 7a and radius be 5a
Now,
Volume = π (5a)2 × 7x
= 14836.5 = (3.14)(25a2) × 7a
= 14836.5 = (3.14)(25a2) × 7a
= 175a3 = \(\frac{14836.5}{3.14 }\)
= a3 = \(\frac{4725}{175}\)
= a = 3
Now, Radius = 5a = 5 × 3 = 15 cm
Height = 7a = 7 × 3 = 21 cm
For TSA of cylinder,
TSA = 2(3.14) × 15 × (15 + 21) = 6.28 × 15 × 36 = 3391.2 cm2