A right triangle ABC with its sides 5 cm, 12cm and 13cm is revolved about the side 12cm. Find the volume of the solid so formed. If the triangle ABC is revolved about side 5cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of  the two solids obtained.

Explanation

`r_1=5 cm`
`h_1=12 cm`
`r_2=12 cm`
`h_2=5 cm`
Volume `V_1=1/3pir_1^2h_1`
`1/3xxpixx5xx5xx12`
`(25xx12)/3pi`
`V_1=100pi`
`V_2=1/3pir_2^2h_2`
`=1/3xxpixx12xx12xx5`
`=(144xx5)/3pi`
`V_2=240pi`
Ratio
`V_1/V_2=100/240`
`V_1/V_2=5/12`
`therefore` The volume of the solid so formed`=100pi` and `240pi`
`therefore` The ratio of the volumes of  the two solids obtained`=5:12`