If the right circular cone is cut into three solids of volumes V1,V2 and V3

Question

If the right circular cone is cut into three solids of volumes

V_{1}, V_{2} a n d V_{3}

by two cuts which are parallel to the base and trisects the altitude, then

V_{1} : V_{2} : V_{3}

is:

Options:

A . 1:2:3

B . 1:4:6

C . 1:6:9

D . None of these

Answer: Option D
:
D
Solution: -

If The Right Circular Cone Is Cut Into Three Solids Of Vol...

The resultant figure is made of three similar triangles. The height and radius will be in ratio

\frac{1}{3} : \frac{2}{3} : 1

= 1:2:3.
r

_{1}

= 1, h

_{1}

= 1
r

_{2}

= 2, h

_{2}

= 2
r

_{3}

= 3, h

_{3}

= 3
Volume will be in the ratio of r\(^2\)h for the three circular cones.
Required Volumes are
V

_{1}

= r

_{1}^{2}

x h

_{1}

= 1
V

_{2}

= r

_{2}^{2}

x h

_{2}

- V

_{1}

= 8 - 1 = 7
V

_{3}

= r

_{3}^{2}

x h

_{3}

- (V

_{1}

+ V

_{2}

) = 27 - (7 + 1) = 19
Volumes will be in given ratio= 1:7:19.Option (d).

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