Question

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Answer 1

Answer:

( 1 : 2 )

Step-by-step explanation:

Assume that the ratio of the altitude of the bigger and the smaller cone be k:1.

Let R and r be the radii of the bigger and the smaller cone respectively.

Let H and h be the height of the bigger and the smaller cone respectively.

Consider the similar triangles △ AGC & △ AFE ,

By the property of similarity, we have

$\frac{\sf{ \rm {curved \:surface \: of \: remaining \: portion}}}{\sf{ \rm {curved \: surface \: of \: whole \: cone}}} = \frac{8}{9}$

$\frac{\sf{ \rm {curved \: surface \: of \: upper \: portion \: of \: cone}}}{\sf{ \rm {curved \: portion \: of \: whole \: cone}}} = \frac{1}{9}$

$\huge { \rm { \frac{\pi \: r \: l}{\pi \: R \: L}}} \: = \frac{1}{9}$

$\frac{r}{R} \times \frac{l}{L} = \frac{1}{9}$

$\frac{h}{H} \times \frac{h}{G} = \frac{1}{9}$

$(\frac{h}{H} )^{2} = ( { \frac{1}{3} )}^{2} \\ \\ ( \frac{h}{H} ) = \frac{1}{3} \\ \\ H \: = \: 3 \: h$

$\sf{ \rm {required \: height = \frac{height \: of \: upper \: portion}{height \: of \: frustum} }} \\ \\ = \frac{h}{3h - h} = \frac{h}{2h} = \frac{1}{2}$

Hence , the ratio is (1:2)

Answer 2

Answer:

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Step-by-step explanation: