Question

A bucket is in the form of frustum of cone and holds 28.490 litres of water the radii of the top and bottom of the bucket are 28cm and 21cm respectively find the height of the bucket.

Answer 1

Let the height of the bucket be h cm.

We have, r1= 28 cm, r2= 21cm

V = volume of the bucket = 28.490 litres = 28.490 x 1000cm3

= 28490 cm3

V =1/3πh{(R)2•(r)2•(R•r)}

Thus, the height of the bucket is 15 cm.

Answer 2

Let the height of the bucket be h cm.

We have, r1= 28 cm, r2= 21cm

V = volume of the bucket = 28.490 litres = 28.490 x 1000cm3

= 28490 cm3

V =  3

1

​  

π(r  

1

2

​  

+r  

2

2

​  

+r  

1

​  

×r  

2

​  

)h

∴28490=  

3

1

​  

×  

7

22

​  

×(28  

2

+21  

2

+28×21)×h

∴28490=  

21

22

​  

×(784+441+588)×h

∴h=  

22×1813

28490×21

​  

=15 cm.

Thus, the height of the bucket is 15 cm.