Question

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former.Find the ratio of their radii I want in stepz plzz

Answer 1

we know, curve surface area of cone is given by, A = πrl

where r is radius of base of cone and l is slant height.

a/c to question,

The curve surface area of one cone is twice that of other.

i.e., $A_1=2A_2$

or, $\pi r_1l_1=2\pi r_2l_2$

or, $r_1l_1=2r_2l_2$....(1)

again, the slant height of later is twice that of former.

i.e., $l_2=2l_1$.....(2)

putting equation (2) in equation (1),

$r_1l_1=2r_2(2l_1)$

or, $r_1=4r_2$

or, $\frac{r_1}{r_2}=\frac{4}{1}$

hence, ratio of their radii is 4 : 1

Answer 2

Answer:

$Ratio \: of \: radii = 4:1$

Step-by-step explanation:

Dimensions of first cone :

Curved surface Area = 2A

slant height = l

Radius = r

Dimensions of the second cone:

Curved surface area = A

Slant height = 2l

Radius = R

/* We know that,

$\boxed {Surface\: Area \: of \: a \: cone \\= \pi \times radius \times slant \: height}$

$Ratio \: of \: Surface\:Areas = \frac{2A}{A}$

$\implies \frac{\pi rl}{\pi R\times 2l}=2$

$\implies \frac{r}{2R} = \frac{2}{1}$

$\implies \frac{r}{R} = \frac{4}{1}$

Therefore,

$Ratio \: of \: radii = 4:1$

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