Question

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 volume the two parts.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

ANSWER

Here , circular base of the upper part and the lower part are parallel.

.

. . Their radii are also parallel.

Let h be the height of the upper part of the cone.

Then AM=MN =h ......... ( M is the midpoint of height AN)

In AMQ and ANC

1.) angle MAQ is congruent to angle NAC ......(common angle )

2.) angle AQM is congruent to angle ACN .....(corresponding angles)

3.) Triangle AMQ is similar to triangle ANC ......(by AA test of similarity)

4.) AM÷AN = MQ÷NC .......(c-s-s-t)

h = r

__ ___

10 NC

1 r

___ = ____

1O NC

NC= 10r

Volume of upper part of cone = 1 π r² h

3

Volume of lower part of cone= Volume of bigger cone- Volume of smaller cone

= 1 π R² H - 1 π r² h

3 3

by solving

= 13 π r² h

The ratio of the volume of upper part and lower part of the cone.

= Volume of upper part of the cone

____________________________

Volume of lower part of the cone

= ⅓πr²h

_______

13πr²h

= 1 1

×

3 13

= 3:13