This question was asked in 2014 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 822, exercise 17C, problem number 3

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# 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.

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Height, h=24 cm,

Upper base radius, R=14 cm

lower base radius, r=7 cm

The slant height, l = √[[R- r]² + h²]

l = √ [[14-7]² + 24²]

= √ [7²+ 24²]

= √[49+576]

= √625

= 25 cm

i) the volume of water which can completely fill the bucket =[1/3] π h [R²+r²+rR]

= [1/3]×[22/7]×24×[14²+7²+[14×7]]

= [22/7]×8×[196+49+98]

= 1767×343

= 8624 cm³

∴ the volume of water which can completely fill the bucket is 8624 cm³

(ii)Curved surface area = πl( R+r)

= [22/7] * 25 * (14+7)

= 1650 cm

^{2}Area of the base of bucket = πr

^{2}= [22/7] * 7

^{2}= 154 cm

^{2}Area of metal sheet used to make the bucket = curved surface area + Area of the base

= 1650 + 154

= 1804

∴ Area of metal sheet used to make the bucket is 1804 cm

^{2}