CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Three balls of equal radius are placed such that they are touching each other. A fourth smaller ball is kept such that it touches the other three. Find the ratio of the radii of smaller to larger ball.

A
(2-√3)/ √3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
3- 2√3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4√5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3+2√5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D (2-√3)/ √3

Option (a)

Let the centers of the large balls be x, y, z and radius R.

O is the centre of the smaller ball and radius r...

x, y, z form an equilateral triangle with side equal to 2R.

O is the centroid of this triangle.

Therefore ox=oy=oz=R+r= 23(height of the triangle xyz)

Height=(32)(2R) =3R

Therefore R+r =23(3R) rR= (23)3


flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image