The radius 3

The radius of a solid circular cylinder decreases by 20% and its height increases by 10% . Find the percentage change its :
(a) volume
(b) curved surface area.

Correct answer:

p₁ =  -29.6 %
p₂ =  -12 %

Step-by-step explanation:

$$\begin{gathered} k_1=100\%-20\%=1-\frac{20}{100}=0.8 \\ {k}_2=100\%+10\%=1+\frac{10}{100}=1.1 \\ {r}_2=k_1\cdot r \\ {h}_2=k_2\cdot h \\ {V}_1=\pi \cdot r^2\cdot h \\ {V}_2=\pi \cdot r_2^2\cdot h_2=\pi (k_1\cdot r{)}^2\cdot (k_2\cdot h)=k_1^2\cdot k_2\cdot V_1 \\ {k}_3=\frac{V_2}{V_1}=\frac{k_1^2\cdot k_2\cdot V_1}{V_1} \\ {k}_3=k_1^2\cdot k_2=0.8^2\cdot 1.1=\frac{88}{125}=0.704 \\ {p}_1=100\cdot (k_3-1)=100\cdot (0.704-1)=-29.6\% \end{gathered}$$

$$\begin{gathered} S_1=2\pi \cdot r\cdot h \\ {S}_2=2\pi \cdot r_2\cdot h_2=2\pi \cdot (k_1\cdot r\cdot (k_2\cdot h)=k_1\cdot k_2\cdot S_1 \\ {k}_4=\frac{S_2}{S_1}=\frac{k_1\cdot k_2\cdot S_1}{S_1} \\ {k}_4=k_1\cdot k_2=0.8\cdot 1.1=\frac{22}{25}=0.88 \\ {p}_2=100\cdot (k_4-1)=100\cdot (0.88-1)=-12\% \end{gathered}$$

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