  Question

Find the volume curved surface area and the total surface area of a cone whose height is $$6\ cm$$ and slant height $$100\ cm$$ (Take $$\pi=3.14$$)

Solution

It is given thatHeight of the cone $$=6\ cm$$Slant height of the cone $$b=10\ cm$$We know thatRadius of the cone $$=\sqrt {(l^{2}-h^{2})}$$By substituting the valuesRadius of the cone $$\sqrt {(10^{2}-6^{2})}$$On further calculationRadius of the cone $$\sqrt{ (100-36)}=\sqrt{ 64}$$So we getRadius of the cone $$=8\ cm$$We know thatVolume of the cone $$=\dfrac{1}{3}\pi r^{2}h$$By substituting the valuesVolume of the cone $$=\dfrac{1}{3}\times 3.14\times 8^{2}\times 6$$On further calculationVolume of the cone $$=401.92\ cm^{2}$$We know that Curved surface area of a cone $$=\pi rl$$By substituting the valuesCurved surface area of a cone $$=3.14\times 8\times 10$$So we getCurved surface area of a cone $$=251.2\ cm^{2}$$We know thatTotal surface area of cone $$=\pi r(l+r)$$By substituting the valuesTotal surface area of cone $$=3.14\times 8\times (10+8)$$On further calculationTotal surface area of cone $$=3.14\times 8\times 18$$So we getTotal surface area of cone $$=424.16\ cm^{2}$$MathematicsRS AgarwalStandard IX

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