Question

If a cone with a diameter of 10 m has a surface area of 190.6m2, find its slant height. Round to the nearest tenth.

Slant Height = m

Answer 1

Answer: The slant height of the cone is 65.6 m

Explanation:

Given: The diameter of a cone = 10 m

Surface area of cone = 190.6 m²

To find: Slant height

Diameter of cone = 10 m

Therefore Radius of cone =
`\frac{\text {Diameter }}{2} = (10)/(2) =5m`

As we know that surface area of a cone is given by

`S.A. = \pi r(l+r)`

Where S.A. is surface area , r is the radius of cone and l is the slant height of the cone.

Let Slant height = l

So we have

`190.6 = (22)/(7) * 5 ( 5+l)\\\\\Rightarrow 5+l= (190.6 * 7)/(22)\\\\\Rightarrow l= (1334.2)/(22)+5\approx 60.64+5 = 65.64\approx65.6`

Hence the slant height of the cone is 65.6 m