Question

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former.The ratio of their radii is

• A. 2:1
• B. 4:1
• C. 8:1
• D. 1:1

Answer 1

The correct option is B

4:1

Let r be the radius and l be the slant height

$\therefore$ Curved surface area of first cone=$\pi r_1{l}_1$

and curved surface area of second cone=$\pi r_2{l}_2$

But $l_2=2l_1$and

$\pi r_1{l}_1=2\pi r_2{l}_2\therefore \frac{\pi r_1{l}_1}{\pi r_2{l}_2}=\frac{2}{1}\frac{r_1{l}_1}{r_2{l}_2}=\frac{2}{1}But{l}_2=2l_1\therefore \frac{r_1{l}_1}{r_{2}2l_1}=\frac{2}{1}\Rightarrow \frac{r_1}{2r_2}=\frac{2}{1}\Rightarrow \frac{r_1}{r_2}=\frac{4}{1}\therefore Ratioofradii=4:1$