Login/Sign Up
Home » The height of a cone is . A small cone is cut off from the top by a plane parallel to the base. If its volume be of the volume of the original cone, determine at what height above the base the section is made.
The height of a cone is 20cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.
CBSE | Class 10 | Exercise 16.3 | Maths | RD Sharma | Surface Areas And Volumes
The height of a cone is 20cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

According to the given information,

Let us asssume the radius of the small cone be r cm

And, the radius of the big cone be R cm

It is given, height of the big cone is 20cm

Let us also assume the height of section made be  h cm

Therefore, the height of small cone will be (20-h)cm

Now according to the question,

In \vartriangle OAB  and \vartriangle OCD

\angle AOB=\angle COD [common]

\angle OAB=\angle OCD [each {{90}^{\circ }}]

Therefore, \vartriangle OAB\sim \vartriangle OCD [by AA similarity]

So, by corresponding part of similar triangles we have,

OA/OC=AB/CD

By subsituiting their value,

(20-h)/20=r/R …… (i)

It is also given in the question that,

Volume of small cone =1/125\times volume of big cone

1/3\pi {{r}^{2}}\left( 20-h \right)=1/125\times 1/3\pi {{R}^{2}}\times 20

{{r}^{2}}/{{R}^{2}}=1/125\times 20/\left( 20-h \right) [From (i)] 

{{\left( 20-h \right)}^{2}}/{{20}^{2}}=1/125\times 20/20-h

{{\left( 20-h \right)}^{2}}={{20}^{3}}/125

20-h=20/5

20-h=4

h=20-4

=16cm

Therefore, 16cm above the base was the height of the section made.

i

More Material