Question

The volume of a sphere is increasing at the rate of 1200c.cm/sec.The rate of increase in its surface area when the radius is 10 cm is.

• A. 120 sq.cm/sec
• B. 240 sq.cm.sec
• C. 200 sq.cm.sec
• D. 100 sq.cm.sec

Answer 1

The correct option is B 240 sq.cm.sec

$V=\frac{4}{3}\pi r^3$

$\frac{dy}{dt}=\frac{4}{3}\pi 3r^2\frac{dy}{dx}$

$\frac{dv}{dt}=4\pi x^2\frac{dx}{dt}$

$240sq.cm$