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.

Answer 1

Answer:  The slant height of the cone is 65.6 m

Step-by-step 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 = $\dfrac{\text {Diameter }}{2} = \dfrac{10}{2} =5m$

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

$190.6 = \dfrac{22}{7} \times 5 ( 5+l)\\\\\Rightarrow 5+l= \dfrac{190.6 \times 7}{22}\\\\\Rightarrow l= \dfrac{1334.2}{22}+5\approx 60.64+5 = 65.64\approx65.6$

Hence the slant height of the cone is 65.6 m