Question #6b9d0
1 Answer
In fact the ratio is
Explanation:
Refer to the figure below
Since the 2 planes divide the cone in 3 parts we can obtain 3 ratios. But I presume that
Just not to create confusion, be noticed that
The volume of a cone is given as
Finding
V_2=V-(V_0+V_1)=(bh)/3-(b_2*(2h)/3)/3=(bh)/3-2/9*(b_2*h)V2=V−(V0+V1)=bh3−b2⋅2h33=bh3−29⋅(b2⋅h)
Notice that
->(b_2)/b=(pi*r_2^2)/(pi*r^2)=(r_2/r)^2→b2b=π⋅r22π⋅r2=(r2r)2 and sincer_2/r=((2cancel(h))/3)/cancel(h)=2/3
=>(b_2)/b=(2/3)^2 =>b_2=4/9*b
So
V_2=(bh)/3-2/9*(b_2*4/9b)=(27bh-8bh)/81 =>V_2=(19*bh)/81
Finding
V_1=V-V_0-V_2=(bh)/3-(b_1*h/3)/3-(19*bh)/81
But as we saw above
b_1/b=((cancel(h)/3)/cancel(h))^2=(1/3)^2 =>b_1=b/9
So
V_1=(bh)/3-b/9*h/9-(19*bh)/81=(27*bh-bh-19*bh)/81 =>V_1=(7*bh)/81
So the asked ratio is
V_1/V_2=((7*cancel(bh))/cancel(81))/((19*cancel(bh))/cancel(81))=7/19