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
Deepak BoraNewbie
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 cm2
Area of the base of bucket = πr2
= [22/7] * 72
= 154 cm2
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 cm2