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A cone has a 70 cm diameter and a $4070 c m 2$ curved surface area, then its slant height will be ____ cm.

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Detailed Solution

A cone has a 70 cm diameter and a

4070 c m 2

curved surface area, then its slant height will be 37 cm.
It is given that the cone is 70 cm in diameter.

∴ d = 70 cm ⇒ r = 35 cm

We know that the curved surface area of a cone is

π r l,

where r is the radius of the base and

l

is the cone's slant height.
Here, the curved surface area is

4070 cm 2 .

∴ C S A = π r l ⇒ 4070 = 227 × 35 × l ⇒ l = 4070110 cm ⇒ l = 37 cm

Therefore the cone’s slant height will be 37 cm.

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