Question

# Two cones with same base radius $$8$$ cm and height $$15$$ cm are joined together along their bases. Find the surface area of the shape so formed (answer to the nearest whole number).

Solution

## When two cones of same base are joined together, the surface of the shape formed will only have the curved surfaced areas visible.We know, curved surface area of a cone $$= \pi rl$$, where $$r$$ is the radius of the cone and $$l$$ is the slant height.As both the cones have the same base and height, they are identical and their curved surface areas are equal.Hence, surface area of this shape $$=$$ Curved surface area of Cone 1 $$+$$ Curved surface area of Cone $$2 = 2\times (\pi rl)$$.Given, $$r$$ $$= 8$$ cm and $$h$$ $$= 15$$ cm. Then, slant height $$l= \sqrt { { r }^{ 2 }+{ h }^{ 2 } } = \sqrt { { 8 }^{ 2 }+15^{ 2 } } =\sqrt { 64+225 } =17$$ cm.Therefore, surface area of this shape $$= 2\times (\pi rl) =2\times \dfrac { 22 }{ 7 } \times 8\times 17=854.86 cm^2\approx 855{ cm }^{ 2 }$$.Hence, the required surface area is $$855 cm^2$$.Mathematics

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