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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,

The slant height, l = âˆš[[R- r]Â² + hÂ²]

l = âˆš [[14-7]Â² + 24Â²]

= âˆš [7Â²+ 24Â²]

= âˆš[49+576]

= âˆš625

= 25 cm

i)Â  the volume of water which can completely fill the bucketÂ =[1/3] Ï€ h [RÂ²+rÂ²+rR]

= [1/3]Ã—[22/7]Ã—24Ã—[14Â²+7Â²+[14Ã—7]]

= [22/7]Ã—8Ã—[196+49+98]

= 1767Ã—343

= 8624 cmÂ³

âˆ´ the volume of water which can completely fill the bucket is 8624 cmÂ³

(ii)Curved surface area = Ï€l( R+r)

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

= 1650 cm2

Area of the base of bucket = Ï€r2

= [22/7] * 72

= 154 cm2

Area of metal sheet used to make the bucket = curved surface area + Area of the base

= 1650 + 154

= 1804

âˆ´ Area of metal sheet used to make the bucket is 1804 cm2

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