Question

The radius and height of a cylinder are in the ratio 3:2 and its volume 19404cm³. Find its radius and height.

Answer 1

Given ratio of radius and height of  a cylinder = 3:2
Let the radius be 3x cm 
and height be 2x cm
Given
Volume of the cylinder  = 19404 cm³
⇒ π r² h = 19404 cm³
⇒ (22/7)× (3x)²× 2x = 19404 cm³
⇒ 22/7 ×  9x²   ×  2x  = 19404 cm³
⇒ 22/7  ×  18x³ = 19404 cm³
⇒  18x³ = (19404 × 7)/22
⇒  18x³ = 6174
⇒  x³ = 6174/18
⇒  x³ = 373
⇒  x = ∛373
∴ x = 7
Radius = 3x = 3×7 = 21cm
 Height = 2x = 2×7 = 14cm