SSC CHSL 2023 PYQ — Question 57

The correct answer is option 3 i.e. 11.23 cm³.

Edge length(s) = $3\frac{1}{2}$ = $\frac{7}{2}$ cm

Base diameter = Edge length of the cube = $\frac{7}{2}$ cm

Radius r of the base = half of the diameter

⇒ r = $\frac{1}{2}\times \frac{7}{2}$ = $\frac{7}{4}$ cm

Height h of the cone = Edge length of the cube

⇒ h = $\frac{7}{2}$ cm

Thus,

The volume of a right circular cone(V) = $\frac{1}{3}$πr²h

⇒ V = $\frac{1}{3}$ × $\frac{22}{7}$ × ($\frac{7}{4}$)² × $\frac{7}{2}$

⇒ V = $\frac{1}{3}$ × $\frac{22}{7}$ × $\frac{49}{16}$ × $\frac{7}{2}$

⇒ V = 11.23 cm³