Question

Water is being filled at the rate of 1 cm³/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm²/sec) at which the wet conical surface area of the vessel increase, is

• A. 5
• B. \(\frac{\sqrt21}{5}\)
• C. \(\frac{\sqrt26}{5}\)
• D. \(\frac{\sqrt26}{10}\)

Answer 1

The Correct Option is A

The correct option is(C): \(\frac{\sqrt26}{5}\).

\(s=\pi{l}=\pi(\frac{h}{5}\sqrt{h^2+\frac{h^2}{25}}=\frac{\pi}{25}\sqrt{26h^2})\)

\(⇒\frac{ds}{dt}(h=10)=\frac{\sqrt26}{5}\)