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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 are $$28$$ cm and $$21$$ cm respectively. Find the height of the bucket.


Solution

Given : Volume $$=28.490$$ litres $$=28490{ cm }^{ 3 }$$
Radius of the top of cone $$={ r }_{ 1 }=28$$ cm.
Radius of the bottom of cone $$={ r }_{ 2 }=21$$ cm.
Find : The height of the bucket.
Volume of frustrum $$=\dfrac { 1 }{ 3 } \pi \left( { r }_{ 1 }^{ 2 }+{ r }_{ 2 }^{ 2 }+{ r }_{ 1 }\times { r }_{ 2 } \right) h$$
$$\therefore 28490=\dfrac { 1 }{ 3 } \times \dfrac { 22 }{ 7 } \times \left( { 28 }^{ 2 }+{ 21 }^{ 2 }+28\times 21 \right) \times h$$
$$\therefore 28490=\dfrac { 22 }{ 21 } \times \left( 784+441+588 \right) \times h$$
$$\therefore h=\dfrac { 28490\times 21 }{ 22\times 1813 } =15$$ cm.
$$\therefore$$ height of the bucket $$ =15$$ cm.

Mathematics

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