Question

2. If the heights of cone and cylinder are in the ratio of 1:4 and the radil of their bases are in the
ratio 4:1, then the ratio of their volumes is-
(a) 1:2
(b) 2:3
(c) 3:4
(d) 4:3​

Answer 1

$\huge \fcolorbox{maroon}{grey}{answer}$

height of the first cone = x so,

height of the second one = 4x

radius of the first cone = 4y and,

the radius of the second one = y now,

volume of first cone

$= \frac{1}{3} \pi {r}^{2} = \frac{1}{3} \pi {x}^{2} \times 4y = \frac{4}{3} \pi {x}^{2} y$

and volume of the second cone

$\frac{1}{3} \pi {(4x)}^{2} y =$

$\frac{1}{3} 16 {x}^{2} y$

$= \frac{16}{3} \pi {x}^{2} y =$

$16( \frac{1}{3} \pi {x}^{2} y)$

ratio between the volume

$\frac{16}{3} \pi {x}^{2} y : \frac{4}{3} \pi {x}^{2} y$

=

$\frac{16}{3} : \frac{4}{3} = 4 : 1$

D = 4:1

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