If the curved surface area of a cone is thric | vedclass

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(A) Let the radius and slant height of the first cone be $r_1$ and $l_1$,and for the second cone be $r_2$ and $l_2$.Given that the curved surface area

Vedclass · Accepted Answer

$81$

Vedclass · Answer

(A) Let the radius and slant height of the first cone be $r_1$ and $l_1$,and for the second cone be $r_2$ and $l_2$.Given that the curved surface area of the first cone is thrice that of the second cone: $\pi r_1 l_1 = 3(\pi r_2 l_2)$.Also,given that the slant height of the second cone is thrice that of the first: $l_2 = 3l_1$.Substituting $l_2$ in the first equation: $\pi r_1 l_1 = 3(\pi r_2 \cdot 3l_1)$.Simplifying: $r_1 l_1 = 9 r_2 l_1$.Dividing both sides by $l_1$: $r_1 = 9r_2$,which implies $\frac{r_1}{r_2} = 9$.The ratio of the area of their bases is $\frac{\pi r_1^2}{\pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2 = 9^2 = 81$.Thus,the ratio is $81:1$.

If the curved surface area of a cone is thrice that of another cone and the slant height of the second cone is thrice that of the first,find the ratio of the area of their bases. (in $:1$)

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