This is one of the important question from the cbse board exam point of view because in 2009 cbse board exam this question was asked. Question number 11 from RS Aggarwal book page number 823, exercise 17C, chapter volume and surface area of solid.
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A bucket is in the form of a frustum of a cone and it can hold 28.49 liters of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket
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Solution
given data
Radius of upper end, R=28 cm
Radius of lower end, r=21 cm
the height of the bucket be h.
Volume of water the bucket can hold=28.49 L
Volume of bucket=28490 cm [ 1 L =1000 cm]
Volume of bucket = [1/3] π h [R²+r²+rR]
[1/3] π h [R²+r²+rR] = 28490
[1/3] × [22/7]×h×[28²+21²+ [28×21]]=28490
22h21×49×16+9+12 = 28490
22h3×7×37=28490
h=28490×322×7×37
∴ h=15 cm
∴ the height of the bucket is 15 cm.