Question

If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then write the ratio of their weights.

Answer 1

The ratio of the volume of cones

`v_1 : v_2 = 1 : 4`

And `2r_1 :2r_2 = 4 : 5,`

i.e., `r_1 / r_2 = 4/5`

`"Now", v_1/v_2 = (1/3 pir_1^2 h_1)/(1/3 pir_2^2 h_2)`

             `1/4 = (r_1/r_2)^2 xx (h_1/h_2)`

           `h_1/h_2 = 1/4 xx 25 /16`

                 `= 25/ 64`

Hence, `h_1 : h_2 = 25 : 64`