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Question 3
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

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Solution

Given, volume of the frustum =28.49L=28.49×1000 cm3 [1L=1000 cm3]
=28490 cm3

Radius of the top (r1)=28 cm
Radius of the bottom (r2)=21 cm

Let height of the bucket = h cm
Now, volume of the bucket
=13πh(r21+r22+r1r2)=28490 [given]

13×227×h(282+212+28×21)=28490h(784+441+588)=28490×3×7221813h=1295×21h=1295×211813=271951813=15 cm

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