Question

A cone of radius 10 is divided into two parts by a plane parallel to its base through the mid-points of its height. Find the ratios of the volume of two parts.

Answer 1

Answer:

1:7

Step-by-step explanation:

let the height of the given cone =h

on dividing it through mid point of height we get

1). frustum of cone with radius R=10 and h= h/2

2). cone with radius r=5 and h= h/2

ratio of volume= V of cone / V of frustum of cone

and we know that,

V of cone =( 1/3) π r^2 h

and

V of frustum of cone = πh/3(R^2+Rr+r^2)

putting the values in formula we get,

{(1/3)πr^2(h/2)} / {(1/3)π (h/2) (R^2+Rr+r^2)}

= (5*5) / (10^2 + 5^2 + 10*5)

=25/175

=1/7

hence the ratio= 1:7