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- The ratio of their radii is4- 34- 13-41-4

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Toppr Admin · Accepted Answer

CSA of 1st cone - CSA of 2nd cone-xA0-x21D2-x3C0-r1l1-x3C0-r2l2-x2234-l2-2l1-x21D2-x3C0-r1l1-2-xD7-x3C0-r2-xD7-2l1-x21D2-r1r2-4-x3C0-rl1-x3C0-rl1-41-x21D2-r1-r2-4-1

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. The ratio of their radii is
$4 : 3$
$4 : 1$
$3 : 4$
$1 : 4$

CSA of 1st cone = CSA of $2 n d$ cone
$\Rightarrow π r_{1} l_{1} = π r_{2} l_{2}$
$∴ l_{2} = 2 l_{1}$
$\Rightarrow π r_{1} l_{1} = 2 \times π r_{2} \times 2 l_{1}$
$\Rightarrow \frac{r_{1}}{r_{2}} = \frac{4 π r l_{1}}{π r l_{1}} = \frac{4}{1} \Rightarrow r_{1} : r_{2} = 4 : 1$

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. The ratio of their radii is4:34:13:41:4

CSA of 1st cone = CSA of 2nd cone ⇒πr1l1=πr2l2∴l2=2l1⇒πr1l1=2×πr2×2l1⇒r1r2=4πrl1πrl1=41⇒r1:r2=4:1

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. The ratio of their radii is
$4 : 3$
$4 : 1$
$3 : 4$
$1 : 4$

CSA of 1st cone = CSA of $2 n d$ cone
$\Rightarrow π r_{1} l_{1} = π r_{2} l_{2}$
$∴ l_{2} = 2 l_{1}$
$\Rightarrow π r_{1} l_{1} = 2 \times π r_{2} \times 2 l_{1}$
$\Rightarrow \frac{r_{1}}{r_{2}} = \frac{4 π r l_{1}}{π r l_{1}} = \frac{4}{1} \Rightarrow r_{1} : r_{2} = 4 : 1$