Question

If the ratio of volumes of two cones is 4 : 7 and the ratio of the radii of their bases is 8 : 9. The ratio of their heights will be ?

1.

81 : 112

2. 32 : 63
3. 36 : 56 
4. 35 : 57

Answer 1

Correct Answer - Option 1 :

81 : 112

Given:

Ratio of volumes of two cones = 4 : 7

Ratio of the radii of their bases = 8 : 9

Formula used:

Volume of cone = πr²h/3

Where, r = radius of cone

h = height of cone

Calculation:

Let the volumes, radius and height of the cone be V₁, V_2, r₁, r₂, h₁ and h₂ respectively.

According to the question,

V₁/V₂ = (π × r₁² × h₁/3)/( π × r₂² × h₂/3)

⇒ 4/7 = (r₁² × h₁ )/(r₂² × h₂)

⇒ 4/7 = (r₁/r₂)² × (h₁/h₂)

⇒ 4/7 = 64/81 × (h₁/h₂)

⇒ h₁/h₂ = 4/7 × 81/64

⇒ h₁/h₂ = 1/7 × 81/16

⇒ h₁/h₂ = 81/112

∴ The ratio of their heights will be 81 : 112.