If the curved surface area of $c o n e_{1}$ is twice the curved surface area of $c o n e_{2}$ , then what's the relation between their radii and slant heights ?

2 r_{1} l_{1} = r_{2} l_{2}

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r_{1} l_{1} = 2 r_{2} l_{2}

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2 r_{2} l_{1} = r_{1} l_{2}

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\frac{2 r_{1}}{l_{1}} = \frac{r_{2}}{2 l_{2}}

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Solution

The correct option is B $r_{1} l_{1} = 2 r_{2} l_{2}$

Let,
the radius of $c o n e_{1}$ be $r_{1}$ .
the radius of $c o n e_{2}$ be $r_{2}$ .
the slant height of $c o n e_{1}$ be $l_{1}$ .
the slant height of $c o n e_{2}$ be $l_{2}$ .

We know that,
Curved surface area of cone
$= π r l$

Given that,
C.S.A of $c o n e_{1}$ = 2 C.S.A of $c o n e_{2}$ .

Now,
$π r_{1} l_{1} = 2 π r_{2} l_{2}$
$\Rightarrow r_{1} l_{1} = 2 r_{2} l_{2}$

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If the curved surface area of cone1 is twice the curved surface area of cone2, then what's the relation between their radii and slant heights ?

The correct option is B r1l1=2r2l2 Let, the radius of cone1 be r1. the radius of cone2 be r2. the slant height of cone1 be l1. the slant height of cone2 be l2. We know that, Curved surface area of cone =πrl Given that, C.S.A of cone1 = 2 C.S.A of cone2. Now, πr1l1=2πr2l2 ⇒r1l1=2r2l2

If the curved surface area of $c o n e_{1}$ is twice the curved surface area of $c o n e_{2}$ , then what's the relation between their radii and slant heights ?