Question

The height of each solid shown above is $7$. The base of solid-I has $6$ sides of equal length, $6$ angles of equal measure, and center $P$. The base of solid-II is a circle with center $Q$. The base of solid-III is a square with center $R$. Which of the following is true?

• A. Solid-I has the greatest volume.
• B. Solid-II has the greatest volume.
• C. Solid-III has the greatest volume.
• D. The volumes of solids I and II are equal.
• E. The volumes of solids II and III are equal.

Answer 1

The correct option is B Solid-II has the greatest volume.

Since the height of all three solids are equal, their volume depends on their base areas(as the volume is base area$\times$ height). Which solid will have more area should have greater volume.

Area of base of solid $1=6\times \frac{1}{2}\times 3\times 3=27$.

Area of base of solid $2=\frac{22}{7}\times 3\times 3=28.3$ (approx).

Area of base of solid $3=\frac{1}{2}\times 6\times 6=18$.

Therefore solid $2$ will have greater volume.