If the volumes of two cones are in the ratio 1:4 and their diameters are in the ratio 4:5, then the ratio of their heights, is (a)   1:5         (b)  5:4       (c)  5:16       (d)  25:64

Explanation

To solve the problem step by step, we will use the given ratios of volumes and diameters to find the ratio of heights of the two cones.

### Step 1: Understand the given ratios
We are given:
- The volumes of two cones \( V_1 \) and \( V_2 \) are in the ratio \( 1:4 \).
- The diameters of the two cones \( D_1 \) and \( D_2 \) are in the ratio \( 4:5 \).

### Step 2: Express the volume ratio mathematically
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