Question

# Find the volume, curved surface area and the total surface area of a cone having base radius $$35\ cm$$ and height $$12\ cm$$.

Solution

## It is given thatRadius of the cone $$=35\ cm$$Height of the cone $$=12\ cm$$We know thatVolume of the cone $$=\dfrac{1}{3}\pi r^{2}h$$By substituting the valuesVolume of the cone $$=\dfrac{1}{3}\times \dfrac{22}{7}\times 35^{2}\times 12$$On further calculationVolume of the cone $$=15400\ cm^{2}$$We know that Slant height $$l=\sqrt {(r^{2}+h^{2})}$$By substituting the values$$l=\sqrt{ (35^{2}+12^{2})}$$On further calculation$$l=\sqrt{ 1369}$$So we get$$l=37\ cm$$We know that Curved surface area of a cone $$=\pi rl$$By substituting the valuesTotal surface area of cone $$=\dfrac{22}{7}\times 35\times (37+35)$$On further calculation Total surface area of cone $$=22\times 5\times 72$$So we getTotal surface area of cone $$=7920\ cm^{2}$$MathematicsRS AgarwalStandard IX

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