Question

Choose the correct answer in each of the following :

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 curved surface area of the cone is $\pi \times r\times l$

So,

Curved surface area of 1 st cone = $\pi \times r_1\times l_1$

Curved surface area of 2 nd cone = $\pi \times r_2\times l_2$

Given, the curved surface area of 1 st cone is twice of the curved surface area of 2 nd cone

$\pi \times r_1\times l_1$ = 2 $\pi \times r_2\times l_2$

$r_1\times l_1$ = 2 $r_2\times l_2$

$l_2=2l_1$

$r_1\times l_1$ = 2 x $r_2\times 2\times l_1$

$\frac{r_1}{r_2}$ = 4:1

(b) 4:1