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Question

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find

(i) the volume of water which can completely fill the bucket;

(ii) the area of the metal sheet used to make the bucket.


Solution

(i). volume of frustum of cone 

=13×π×h×(R2+Rr+r2)=13×227×24×(142+14×7+72)=22×87×(196+98+49)=22×87×343=22×8×49=8624 cm3

(ii) slant height of frustum, 

l=(Rr)2+h2=(147)2+242=72+242=49+576=625=25 cm

area of metallic sheet = CSA of frustum + area of base

=π×l×(R+r)+π×r2=227×25×(14+7)+227×72=5507×21+22×7=550×3+154=1650+154=1804 cm2


Mathematics
Secondary School Mathematics X
Standard X

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