A) \( \Large 3H \left(P+Q+\sqrt{PQ}\right) \) |
B) \( \Large H \left(P+Q+\sqrt{PQ}\right) \) |
C) \( \Large H \frac{ \left(P+Q+\sqrt{PQ}\right) }{3} \) |
D) \( \Large H \frac{ \left(P+Q-\sqrt{PQ}\right) }{3} \) |
C) \( \Large H \frac{ \left(P+Q+\sqrt{PQ}\right) }{3} \) |
We know that,
Volume of frustum
= \( \Large \frac{\pi H}{3} \left(R^{2} + r^{2} + Rr\right) \)
= \( \Large \frac{ \pi }{3}H \{ \left(\sqrt{\frac{Q}{ \pi }}\right)^{2} + \left(\sqrt{\frac{P}{ \pi }}\right)^{2} + \sqrt{\frac{Q}{ \pi }} - \sqrt{\frac{P}{ \pi }} \} \)
= \( \Large \frac{ \pi H}{3} \{ \frac{Q}{ \pi } + \frac{P}{ \pi } + \frac{\sqrt{PQ}}{ \pi } \} \)
= \( \Large \frac{H}{3} \left(P + Q + \sqrt{PQ}\right) \)