Air is being pumped into a balloon in the shape of a sphere so that its volume is increasing at a constant rate of $$\(50 \mathrm{~cm}^{3} \mathrm{~s}^{-1}\)$$. Find the rate at which the radius of the balloon is increasing when the radius is $$\(10 \mathrm{~cm}\)$$. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_w20_qp_11 Year：2020 Question No：3
Answer:
\((\) Derivative \(=) 4 \pi r^{2}(\rightarrow 400 \pi)\)
\(\frac{50}{\text { their } \text { derivative }}\)
\(\frac{1}{8 \pi}\) or \(0.0398\)
\(\frac{50}{\text { their } \text { derivative }}\)
\(\frac{1}{8 \pi}\) or \(0.0398\)
Knowledge points:
1.7.3 apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (Including connected rates of change, e.g. given the rate of increase of the radius of a circle, find the rate of increase of the area for a specific value of one of the variables.)
Solution:
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