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Question

Two cones with same base radius $$8cm$$ and height $$15cm$$ are joined together along their bases. Find the surface area of the shape so formed.


Solution


When two identical cones are joined base to base, the total surface area of new solid becomes equal to the sum of curved surface areas of both the cones.

So, total surface area of solid = $$\pi rl + \pi rl = 2\pi rl$$

In two cones, $$r = 8 cm, h = 15 cm$$

Now, $$l^{2} = r^{2} + h^{2} = 8^{2} + 15^{2} = 64 + 225 = 289$$

$$\Rightarrow l^{2} = (17)^{2}$$

$$\Rightarrow l = 17cm$$

$$\therefore$$ Total surface area of solid = $$2\pi rl$$

$$= 2 \times \pi  \times 8 \times 17$$

$$= 272\pi cm^{2}$$

$$= 854.857 cm^{2}$$

Hence, the surface area of new solid $$= 854.857 cm^{2}$$.



Mathematics

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