Question

A cone of height 2.8 cm has a lateral surface area 23.10 cm^2.what is the radius of the base.please solve it urgently.please .please

Answer 1

lateral surface area is given by π R L    L = lateral length or lateral height
L² = R² + H²            H = height of cone
L²   =  R² + 2.8²    ----- equation 1

23.10 = 3.14 * R * L
R L = 7.353  cm²
L  = 7.353 / R

Substitute in equation 1

7.353² /R² = R² + 2.8²

R^4 + 7.84 R² - 54.066  = 0

Δ =  277.73
R²  =  4.412

R = 2.1  cm
L = 3.5 cm

Answer 2

lateral surface area is given by πrl    l = lateral height
l² = r² + h²            h = height of cone = 2.8 cm
l = √ (r² + 2.8²)    -----  i

23.10 = 3.14 × r × l
rl = 7.353  cm²
l  = 7.353 / r

So

7.353/r = √(r² + 2.8²)
7.353² /r² = r² + 2.8²  

r⁴ + 7.84r² - 54.066  = 0 

solving r

r = 2.1003 cm