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Question

The volume of a cylinder is $$308\ cm^{3}$$. Its height is $$8\ cm$$. Find its lateral surface area and total surface area.


Solution

Let $$r$$ be the radius of cylinder.
Volume of cylinder $$= 308 \; {cm}^{3} = \pi {r}^{2} h$$
$$\Rightarrow \cfrac{22}{7} \times {r}^{2} \times 8 = 308$$
$$\Rightarrow {r}^{2} = \cfrac{308 \times 7}{22 \times 8}$$
$$\Rightarrow r = \sqrt{\cfrac{49}{4}} = \cfrac{7}{2} \; cm$$
Therefore,
Lateral surface area of cylinder $$= 2 \pi rh \\ = 2 \times \cfrac{22}{7} \times \cfrac{7}{2} \times 8 \\ = 176 \; {cm}^{2}$$
Also,
Total surface area of cylinder $$= 2 \pi r \left( h + r \right) \\ = 2 \times \cfrac{22}{7} \times \cfrac{7}{2} \times \left( 8 + \cfrac{7}{2} \right) \\ = 22 \times \cfrac{23}{2} = 253 \; {cm}^{2}$$

Mathematics

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