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

The side of a square is $22 \, m$. What is the radius of the circle whose circumference is equal to the perimeter of the square? (in $m$)

The circumference of a circle is $176\, m$. Then,its area is

If the length and breadth of a rectangular room are each increased by $1\, m$,then the area of the floor is increased by $21\, m^2$. If the length is increased by $1\, m$ and the breadth is decreased by $1\, m$,then the area is decreased by $5\, m^2$. The perimeter of the floor is.......$m$.

Two circles touch each other externally. The sum of their areas is $130 \pi \text{ cm}^2$ and the distance between their centres is $14 \text{ cm}$. The radius of the smaller circle is . . . . . . $\text{cm}$.

The number of marble slabs of size $20 \text{ cm} \times 30 \text{ cm}$ required to pave the floor of a square room of side $3 \text{ m}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module