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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