Question

The height of a cone is 60 cm.a small is cut off at the top by a pane parallel to the base and its volume of original cone.find the height from the base at which the section is made.

Answer 1

☆☆☆ranshsangwan☆☆

let r1 be radius of new cone

& let h1 be height of new cone

let r2 be radius of old cone

now both the cones are similar

so

r1/r2=h1/60=t

V1=h1r12(pi)/3

V2=60r22(pi)/3

V1/ V2=(h1/60)*(r1/r2)2

V1/ V2=t3

1/ 64=t3

t=1/4

(h1/60)=1/4

h1=15 cm

height of new cone is 15cm

so height of the section is 60-15=45 cm

Answer 2

Height of the original cone= H=60cm

Let height of small cone(that is cut)be 'h '

--> h/H=r/R (by similar triangles prop.)(AAA similarity) ---- (1)

Ratio of volumes--> v/V=r^2*h/R^2*H

As proved in (1),

v/V=r^3/R^3

1/64=r^3/R^3

Taking cube root of both sides,

r/R=1/4-- (2)

Substitute (2) in (1),

h/60=1/4

h=60/4

h=15 cm

Therefore, small cone is cut (60-15)= 45 cm above the base of the cone

I hope it helps u dear.......