The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

# The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

1. A
1:7
2. B
7:1
3. C
2:7
4. D
7:2

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### Solution:

Given,
Height of cone is 10cm.
According to the question, the figure will be,
Here, the upper part is a cone and the lower part is a frustum.
Now, in the figure
In triangle OCD and OAB,
[Same angle]
[Right angles]
[Corresponding angles]
Thus,
So,
Now, the height of the smaller cone is half the height of the original cone.
So,
We get,
The volume of a cone of radius r and height h is given by  .

Thus, the volume of upper part is
The volume of the frustum of cone is given by
We get,

Thus, the volume of lower part is  .
The ratio of the volume of the upper part to the volume of the lower part of the original cone is given by,
Thus, the ratio of the volumes of two parts is 1:7.
Hence, the correct option is 1

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