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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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