A metallic bucket open at the top of height 24 cm is I the form of frustum of a cone the radii of whose lower and upper ends are 7 cm and 14 cm respectively find
volume of the water that can fill the bucket
Volume of feustum= volume of one OCD−OAB
⇒13πr22h2−13πr21h1
=π3(142h2−72h1)
π3×72(4h2−h1)
Now, In △OMB,∠OBM=∠ODN(MB||ND),∠OMB−∠OND=90o,∠O=∠O By AA simplify △OMB∼△ONB.
⇒h1h2=r1r2 ⇒h1h2=714=12 ⇒2h1
Now, h2−h1=24⇒2h1−h1=24⇒h1=24cm,h2=48cm
⇒ volume =49π3(8h1−h1)=49π3×7×248
=49×56π=8616.16 cm3