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Question

The surface area of a cylinder varies jointly as the radius, and the sum of the radius and the height. A cylinder with height $$8\ cm$$ and radius $$4\ cm$$ has a surface area of $$96\pi cm^{2}$$. Find the surface area of a cylinder with radius $$3\ cm$$ and height $$10\ cm$$


Solution

It is given that the area $$A$$ of a cylinder varies jointly as the radius $$r$$ and the sum of the radius and height $$(r+h)$$ and $$A=96π$$ cm$$^2$$ when $$r=4$$ cm and $$h=8$$ cm, therefore,

$$A=kr(r+h)\\ \Rightarrow 96π=k\times 4(4+8)\\ \Rightarrow 96π=k\times 4\times 12\\ \Rightarrow 48k=96π\\ \Rightarrow k=\frac { 96π }{ 48 } =2π$$   

Thus, the general equation is $$A=2πr(r+h)$$.

Since $$r=3$$ cm and $$h=10$$ cm, therefore,

$$A=2πr(r+h)=2π\times 3(3+10)=2π\times 3\times 13=78π$$

Hence, the surface area of the cylinder with radius $$3$$ cm and height $$10$$ cm is $$78π$$ cm$$^2$$

Mathematics

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