A spherical balloon is pumped at the rate of 10inch3min

A spherical balloon is pumped at the rate of $10 i n c h^{3} / m i n$ , the rate of increase of its radius if its radius is 15 inch is

A. $\frac{1}{30 π} i n c h / m i n$

$\frac{1}{60} i n c h / m i n$

$\frac{1}{90} i n c h / m i n$

$\frac{1}{120} i n c h / m i n$

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

Let V be the volume and r the radius of the ballon at any time t.
$∴ V = \frac{4}{3} π r^{3} ∴ \frac{d V}{d t} = \frac{4}{3} π (3 r^{2}) \frac{d r}{d t} \Rightarrow 10 = \frac{4 π}{3} .3 . (15)^{2} \frac{d r}{d t} ∴ \frac{d r}{d t} = \frac{1}{90 π} i n c h / m i n$

A spherical balloon is pumped at the rate of 10inch3min

Right Answer is: C

SOLUTION

Related QuestionsIf a particle moving along a line follows the law s=√1+If V=43πr3at what rate in cubic units is V increasing wA man of height 2m walks directly away from a lamp of hA ladder20 ft long has one end on the ground and the ot

Related Questions
If a particle moving along a line follows the law s=√1+
If V=43πr3at what rate in cubic units is V increasing w
A man of height 2m walks directly away from a lamp of h
A ladder20 ft long has one end on the ground and the ot