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Maths-

General

Easy

Question

A spherical balloon is being inflated at the rate of 30 $c c to the power of blank divided by m i n$ . The rate of increase of the surface area of the balloon when its diameter is 14cm, is

7 sq cm/min
10 sq cm/min
17.5 sq cm/min
28 sq cm/min

The correct answer is: 10 sq cm/min

Let volume of sphere( $V$ )= $fraction numerator 4 over denominator 3 end fraction pi r to the power of 3 end exponent$
$rightwards double arrow fraction numerator d V over denominator d t end fraction 4 pi r to the power of 2 end exponent fraction numerator d r over denominator d t end fraction blank rightwards double arrow fraction numerator d r over denominator d t end fraction equals fraction numerator 35 over denominator 4 pi r to the power of 2 end exponent end fraction$

Let surface area of sphere(S) $equals 4 pi r to the power of 2 end exponent$

$rightwards double arrow fraction numerator d S over denominator d t end fraction equals 2 cross times a pi r fraction numerator d r over denominator d t end fraction$

$blank equals 2 cross times 4 pi r cross times fraction numerator 35 over denominator 4 pi r to the power of 2 end exponent end fraction$

$therefore blank fraction numerator d S over denominator d t end fraction equals 10 s q blank c m divided by m i n$

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