  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 thatSurface 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 thatVolume of cylinder $$=\pi r^2 h$$By substituting the valuesVolume of cylinder $$=\dfrac{22}{7}\times (17.5)^2 \times 40$$So we getVolume of cylinder $$=38500\ cm^3$$Therefore, the height of the cylinder is $$40cm$$ and the volume is $$38500\ cm^3$$.MathematicsRS AgarwalStandard IX

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