The radii of the two ends of a pail of height 24 cm are 15 cm and 5 cm . Find the volume of the pail .

Explanation

The volume of the pail = (Volume of the conical OAB) - (Volume of the cone OCD)
Now , `Delta OPB ~ Delta OQD`
` :. (PO)/(OQ) = (PB)/(QD) `
`rArr (h_(1))/(h_(2)) = 15/2 = 3 `
` rArr h_(1) = 3h_(2)`
Again , `PQ = OP - OQ`
` h_(1) - h_(2) = 24 `
` rArr 3h_(2) - h_(2) = 24`
` rArr 2h_(2) = 24`
` rArr h_(2) = 24/2 `
` rArr h_(2) = 12 `
` :. h_(1) = 3h_(2) = 3xx12 = 36`
So , the volume of the OAB `= 1/3 xx 22/7 xx 15^(2) xx 36 ` cc
` 22/7 xx 5 xx 15 xx 36 ` cc
and the volume of the cone OCD ` = 1/2 xx 22/7 xx5^(2) xx 12 ` cc
` = 22/7 xx 5xx 5xx 4 ` cc
` :.` the volume of the pail ` = (22/7 xx 5 xx 15 xx 36 - 22/7 xx 5xx 5 xx 4)` cc
` = 22/7 xx 5 (15 xx 36 - 5 5 xx 4) ` cc
` = 22/7 xx 5 (540 - 20 ) "cc" = 22/7 xx 5 xx 520 ` cc
` (57200)/7 " cc" = 8171 3/7 ` cc
Hence the volume of the pail `= 8171 3/7 ` cc