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).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3391.2 cm2.
Let the height and radius of the cylinder be 7x and 5x respectively.
Its volume is 14836.5 cm3
Formula used
Volume of the cylinder = π r² h
Total surface area of the cylinder = 2π r h + 2π r²
Calculation
⇒ π r² h = 14836.5
⇒ 3.14 × (5x)2 × 7x = 14836.5
⇒ 175 x3 = 14836.5/3.14 = 4725
⇒ x3 = 4725/175 = 27
⇒ x = 3
⇒ Radius r = 5x = 5 × 3 = 15 cm
⇒ Height h = 7x= 7 × 3 = 21 cm
⇒ Total surface area of the cylinder = 2π × 15 × 21 + 2π 15² = 2 × 3.14 × 15 × (21 + 15) = 3391.2 cm2