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Question

If the radii of the circular ends of a conical bucket which is 45cm high be 28cm and 7cm, find the capacity of the bucket?


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Solution

Step1: Sate the given data and formula used

It is given that, the height AC of the conical bucket is 45cm.

Also, it is given that the radii of the bucket are,

r1AB=28cm

r2CD=7cm

We know that,

The volume of the conical bucket =13πr12+r22+r1r2h,

Where, h is the height of the conical bucket and r1,r2 are the radii of the top and the bottom of the bucket.

Step 2: Calculate the required volume

Now, the volume of the conical bucket can be calculated as,

The volume of the conical bucket =13πr12+r22+r1r2h

=13×227×282+72+287×45

=227×784+49+196×15

=227×1029×15

=22×147×15

=48510cm3

Hence, the capacity of the given bucket is 48510cm3.


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