Question

A cone has a circular base of radius 8m. Given that the total surface area of the cone is 350m^2, find the slant height

Answer 1

Hello There!!

Given

Radius of Circular Base Of Cone= 8m

Total Surface Area= 350m²

Considering Slant Height as l

Solving

We know,

Total Surface Area= Curved Surface Area of Cone+ Area of circular Base

i.e.,

$350 { \text{m}}^{2} = \pi \times r \times l + \pi \times {r}^{2}$

$350 = \pi \times r(l \times r) \\ \\ \implies 350 = 3.142 \times 8(l + 8) \\ \\ \implies \frac{350}{3.142 \times 8} = l + 8 \\ \\ \implies 13.924 = l + 8 \\ \\ \implies l = 13.924 - 8 \\ \\ \therefore l = 5.924 \: \text{cm}$

So, Slant Height= 5.924 cm

Hope This Helps