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

2:3

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8:5

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5:8

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Solution

The correct option is B 8:5
Given that,
r:h = 3:4
Let r = $3 x$ and h = $4 x$

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

The Slant height:
$l = \sqrt{(3 x)^{2} + (4 x)^{2}}$
$\Rightarrow l = 5 x$

We know that,
Total surface area of cone
$= π r (r + l)$
Curved surface area of cone
$= π r l$

Hence, the required ratio
$= \frac{T o t a l s u r f a c e a r e a o f c o n e}{C u r v e d s u r f a c e a r e a}$

$= \frac{π r (r + l)}{π r l}$

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

$= 8 : 5$

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