Question

The height of the two right circular cones is in the ratio 3 : 2. The circumference of the base circle of those two cones is in the ratio 1 : 2 . If the volume of the cones are in the ratio 1 : k, what is the value of k?
1. 4/3
2. 2
3. 7/3
4. 8/3

Answer 1

Correct Answer - Option 4 : 8/3

Calculation:

The volume of cone = constant × R²H

The circumference is in the ratio 1 : 2.

∴ radiuses are r and 2r

Also, the heights are 3h and 2h

⇒ volumes are in the ratio =  r² × 3h : (2r)² × 2h

⇒ 3r²h : 8r²h

⇒ 3 : 8

⇒ 1 : 8/3

∴ k = 8/3

The circumference is proportional to radius/diameter.

The total surface area of a right circular cone of slant height L and radius r is given by πr(L + r).

The volume of the right circular cone is given by πr2h/3, where h is the height of the cone.