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Deepak Bora
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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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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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  1. 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

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