Question

the radius and slant height of a cone are in the ratio 4:7.if its curved surface area is 792 cm square . find its radius

Answer 1

Given that :
r:l = 4:7
r/l = 4/7
l = (7/4)r

C.S.A = 792 cm²
r = ?

C.S.A of cone = πrl
πrl = 792

(22/7) (r) (7/4)r = 792
r² = 144
r = √144
r = 12 cm
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Answer 2

Hi there !!

Lets assume that the radius and slant height as :

Radius = r = 4x

slant height = l = 7x

Given : 

C.S.A = πrl = 792 cm²

$\frac{22}{7}$ × $4x$ ×$7x = 792cm^{2}$



22  × 4x² = 792 cm²

4x² = 792 ÷ 22

x² = 792 ÷ (22 × 4)

x² = 792 ÷ 88

x² = 9 cm

x = √9

x = 3 cm

Radius = r = 4x 
  
            = 4 ×3
          
            = 12 cm