Please submit your concern

Question:

In a right circular cone, the radius of the base is 14 cm and the height is 48 cm. A cross-section is made through the midpoint of the height parallel to the base. The volume of the upper portion is:

(Take π = 22/7).

Explanation:

We know, for frustum of a cone ratio of volume of smaller cone to bigger cone is cube of the ratio of heights.

∴ $\frac{\mathrm{Volume} \mathrm{of} \mathrm{smaller} \mathrm{cone}}{\mathrm{Volume} \mathrm{of} \mathrm{larger} \mathrm{cone}}$ = ${\left(\frac{\mathrm{h}/2}{\mathrm{h}}\right)}^3$ = $\frac{1}{8}$

⇒ Volume of smaller cone = $\frac{1}{8}$ × $\frac{1}{3}$πr2h

⇒ Volume of smaller cone = $\frac{1}{8}$ × $\frac{1}{3}$ × $\frac{22}{7}$ × 142 × 48 = 1232

Hence, option (b).