The base radii of two right circular cones of the same height are in the ratio 5:5. Find the ratio of their volumes.

Explanation

Given: The base radii of two right circular cones of the same height are in the ratio `5:5`.
Let `r_1` and `r_2` be the radii of two cones and `V_1` and `V_2` be their volumes.
Let `h` be the height of the two cones.
Then,
`V_1=1/3pir_1^2h` and `V_2=1/3pir_2^2h`
Therefore,
`V_1/V_2=(r_1^2)/r_2^2=5^2/5^2=25/25=1/1`
Hence, the ratio of the volumes of two cones is `1:1.