Question

The Radius and height of a cone are in the ratio 3:4. if its volume is 301.44 cm cube what is its radius. find it's curved surface area.

Answer 1

The ratio of the radius and height of the cone is 3:4. Let the radius be 3x and height be 4x

Volume of the cone V = 1/3πr2h  =>  1/3(3.14)(3x)2(4x)= 301.44  =>  1/3*3.14*9*4x3 = 301.44

 => x3 = 8  =>  x=2 

Curved suraface area of the cone =πrl (l= slatn height) , l = √(r2+h2) = √(9x2+16x2)= 5x

πrl= 3.14*3x*5x= 3.14*15*4 = 188.4 cm2

Answer 2

let the ratio be multiplied by x
radius = 3x
height = 4x
3x+4x=7x
radius = 3*7=21 cm
height = 4*4=28 cm
volume of cone =1/3pie r2
301.44=1/3*22/7*r2
301.44=1.04*r2
r2=301.44/1.04
r2=289.8
r=root 289.8
r=17.0 cm
curves surface are of cone = l2=r2+h2
= l2=17.0*17.0+28*28
= l2=289+784
= l2=1073
=l=root 1073
=l=32.7 cm
curved surface area of cone = pie r(l+r)
= 22/7*17.0(32.7+17.0)
=53.4(49.7)
=2653.9 cm2
this is the final answer