One of the important question for the board exam class 10 from mensuration chapter.
This question is from r d sharma class 10 maths.
chapter-16 question number-16 maths r d sharma,mensuration.
In this question we have to find the radius of the base of the cone having a copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm.
Given,
Radius of the copper sphere = 3 cm
We know that,
Volume of the sphere = 4/3 π r3
= 4/3 π × 33 ….. (i)
Also, given that the copper sphere is melted and recasted into a right circular cone
Height of the cone = 3 cm
We know that,
Volume of the right circular cone = 1/3 π r2h
= 1/3 π × r2 × 3 ….. (ii)
On comparing equation (i) and (ii) we have,
4/3 π × 33 = 1/3 π × r2 × 3
r2 = 36
r = 6 cm
Therefore, the radius of the base of the cone is 6 cm.