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The Height of a Cone is 20 Cm. 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. - Mathematics

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Question

The height of a cone is 20 cm. 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.

Solution

We have the following situation as shown in the figure

Let VAB be a cone of height h1 = VO1 =20cm. Then from the symmetric triangles VO 1A and VOA1, we have

`(VO_1)/(VO)=(O_1A)/(OA_1)`

⇒`20/(VO)=(O_1A)/(OA_1)`

It is given that, volume of the cone VA1O is`1/125`times the volume of the cone VAB. Hence, we have

`1/3piOA_1^2xxVO=1/125xx1/3piO_1A^2xx20`

⇒`((OA_1)/(O_1A))^2xxVO=4/25`

⇒`((VO)/20)^2xxVO=4/25`

⇒`VO^3=(400xx4)/25`

⇒ VO3 = 16 x 4

⇒ VO = 4

Hence, the height at which the section is made is 20 − 4 = 16 cm.

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Ex. 14.3 | Q: 6 | Page no. 78
Solution The Height of a Cone is 20 Cm. 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. Concept: Volume of a Combination of Solids.
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