The radius and height of a right cone are in the ratio 3:4.
Then the ratio of total surface area to curved surface of the cone is

2:3

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3:5

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7:9

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8:5

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Solution

The correct option is D
8:5

Given:
$r : h = 3 : 4$

Let
$r = 3 x a n d h = 4 x$

From the relation
$l^{2} = h^{2} + r^{2}$

$l = \sqrt{(3 x)^{2} + (4 x)^{2}}$

$\Rightarrow l = 5 x$

Required ratio
$= \frac{π r (r + l)}{π r l}$

$= \frac{π \times 3 x (3 x + 5 x)}{π \times 3 x \times 5 x}$

$= 8 : 5$

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The radius and height of a right cone are in the ratio 3:4. Then the ratio of total surface area to curved surface of the cone is

The correct option is D 8:5 Given: r:h=3:4 Let r=3x and h=4x From the relation l2=h2+r2 l=√(3x)2+(4x)2 ⇒l=5x Required ratio =πr(r+l)πrl =π×3x(3x+5x)π×3x×5x =8:5

The radius and height of a right cone are in the ratio 3:4.
Then the ratio of total surface area to curved surface of the cone is