• 0
Newbie

# 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.

• 0

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

Share

1. Height, h=24 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

• 0