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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.

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Solution

If two cones with same base and height are joined together along their bases, then the shape so formed looks like the figure shown below.

Given:
Radius of cone, r = 8 cm and
Height of cone, h = 15 cm

So, surface area of the shape so formed
= Curved area of first cone + Curved surface area of second cone
= 2.(Surface area of cone) [Since both cones are identical]
=2×πrl=2×π×r×r2+h2 (l=r2+h2)=2×227×8×(8)2+(15)2=2×22×8×64+2257=44×8×2897=59847=854.85 cm2=855 cm2 (approx)
Hence, the surface area of the shape so formed is 855 cm2.

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