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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $:1$)

Similar Questions

One side of a parallelogram is $10\, m$ and the corresponding altitude is $7\, m$. The area of the parallelogram is......$m^2$

Perimeter of a rhombus is $2p$ units and the sum of the lengths of its diagonals is $m$ units,then the area of the rhombus is

The area of a parallelogram is $72 \, cm^{2}$ and its altitude is twice the corresponding base. The length of the base is.....$cm$.

The area of a trapezium is $2500 \, m^2$. One of its parallel sides is $75 \, m$. If the distance between the two parallel sides is $40 \, m$,then find the length of the other parallel side in $m$.

If the altitude of an equilateral triangle is $12 \sqrt{3} \text{ cm}$,then its area would be

Vedclass Test Series

Exam Paper Generator

Online Exam Module