A weather balloon in the shape of a sphere is being inflated by a pump. The volume of the balloon is increasing at a constant rate of $$\(600 \mathrm{~cm}^{3}\)$$ per second. The balloon was empty at the start of pumping. Find the rate of increase of the radius after 30 seconds. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：3(b)
Answer:
\[
\frac{\mathrm{d} V}{\mathrm{~d} r}=4 \pi r^{2}
\]
\[
\frac{\mathrm{d} r}{\mathrm{~d} t}=\frac{\mathrm{d} r}{\mathrm{~d} V} \times \frac{\mathrm{d} V}{\mathrm{~d} t}=\frac{600}{4 \pi r^{2}}
\]
\(\frac{\mathrm{d} r}{\mathrm{~d} t}=0.181 \mathrm{~cm}\) per second
\frac{\mathrm{d} V}{\mathrm{~d} r}=4 \pi r^{2}
\]
\[
\frac{\mathrm{d} r}{\mathrm{~d} t}=\frac{\mathrm{d} r}{\mathrm{~d} V} \times \frac{\mathrm{d} V}{\mathrm{~d} t}=\frac{600}{4 \pi r^{2}}
\]
\(\frac{\mathrm{d} r}{\mathrm{~d} t}=0.181 \mathrm{~cm}\) per second
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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