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Question

The curved surface area pf a cylinder is $$440\ cm^{2}$$ and the circumference of its base is $$110\ cm$$. Find the height and the volume of the cylinder.


Solution

Consider $$r$$ as the radius as $$h$$ as the height of cylinder 

It is given that

Surface area of cylinder $$=2\ \pi rh$$

By substituting the values

$$2\ \pi rh =4400 ....(1)$$

It is given that circumferences of its base $$=2\ \pi rh$$

So we get

$$2\ \pi rh =110$$

We know that

$$\dfrac{2\ \pi rh }{ 2\ \pi r}=\dfrac{4400}{110}$$

On further calculation

$$h=40 cm$$

Substituting the value of $$h$$ in $$(1)$$

We get

$$2\times \dfrac{22}{7}\times r \times 40=4400$$

On further calculation $$r=\dfrac{4400 \times 7}{44\times 40}$$

So we get

$$r=17.5 cm$$

We know that

Volume of cylinder $$=\pi r^2 h$$

By substituting the values

Volume of cylinder $$=\dfrac{22}{7}\times (17.5)^2 \times 40$$

So we get

Volume of cylinder $$=38500\ cm^3$$

Therefore, the height of the cylinder is $$40cm$$ and the volume is $$38500\ cm^3$$.

Mathematics
RS Agarwal
Standard IX

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