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.

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Solution

Curved surface area, $A_{1} = π L_{1} r_{1}$
$A_{1} = 2 A_{2} = 2 π L_{2} r_{2}$
$π r_{1} L_{1} = 2 π r_{2} 2 L_{1}$
$r_{1} = 4 r_{2}$
$\frac{r_{1}}{r_{2}} = 4$

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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.

Curved surface area,A1=πL1r1A1=2A2=2πL2r2πr1L1=2πr22L1r1=4r2r1r2=4

Curved surface area, $A_{1} = π L_{1} r_{1}$
$A_{1} = 2 A_{2} = 2 π L_{2} r_{2}$
$π r_{1} L_{1} = 2 π r_{2} 2 L_{1}$
$r_{1} = 4 r_{2}$
$\frac{r_{1}}{r_{2}} = 4$