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Mathematics

The radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. Then their volumes are in the ratio:

  1. 3 : 4

  2. 4 : 3

  3. 8 : 9

  4. 9 : 8

Mensuration

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Answer

For cylinder,

Radius = 3a

Height = 2b

Volume of cylinder, v = πr2h = π × (3a)2 × 2b = π × 9a2 × 2b = 18πa2b

For cone,

Radius = 4a

Height = 3b

Volume of cone, V = 13πr2h\dfrac{1}{3}π \text{r}^2 \text{h}

=13π(4a)23b=π×16a2b= \dfrac{1}{3}π (\text{4a})^2 \text{3b} \\[1em] = π \times 16\text{a}^2 \text{b} \\[1em]

∴vV=π×18a2bπ×16a2b=1816=98\therefore \dfrac{\text{v}}{\text{V}} = \dfrac{π \times 18\text{a}^2 \text{b}}{π \times 16\text{a}^2 \text{b}} \\[1em] = \dfrac{18}{16} \\[1em] = \dfrac{9}{8}

= 9 : 8

Hence, option 4 is the correct option.

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