Question

the radius and height of a cone are in the ratio 4:3 . the area of its base is 154cmfind its csa

Answer 1

We have given the ratio of radius and height 4 : 3
Say Radius = 4x
Height = 3x
Slant Height = root [(4x)2 +(3x)2 ]=5x { as it goes to Pythagorean Theorem}

as we know, Area of Base = pie X radius2 =>154=22/7 X 16x2

so solving the eq we get x=1.75cm

Radius=7 , Height =5.25cm, Slant Height =8.75cm

So csa or Curved Surface Area = pie X radius x slant height = 22/7 X 7 X 8.75 x=192.5cm2 (ans)

Answer 2

radius:height = 4:3
r=4x; h=3x.
base is circle, area of circle=π*r²=154cm²
22/7*r*r=154(solve it)
r=7cm.
4x=7(as ratio is 4:3) ⇒x=1.75
height=3x=3*1.75=5.25.

C.S.A=π r l
l=∛h²+r²
l=∛(5.25)²+49
l=∛76.5625
l=8.75 cm.

C.S.A=22*8.75*7÷ 7
C.S.A=192.5 cm²