A sphere of radius 7cm with centre C and a larger sphere with centre E touches each other two common planks to both the spheres have an angle of 60 degree in between them.Then find the radius of larger sphere.
Answers
Given : A sphere of radius 7 cm with centre C and a larger sphere with centre E touches each other, two common planks to both the spheres have an angle of 60° in between them.
To find : the radius of larger sphere.
Solution:
Angle between planks ( tangents) = 60°
Half of angle = 60/2 = 30°
Let Say Distance of Common plank point = d
Sin 30° = 7/( 7 + d)
=> 1/2 = 7/(7 + d)
=> 7 + d = 14
=> d = 7
Distance of center of sphere from common plank point
= d + 2 * 7 + r ( r = radius of larger sphere)
= 7 + 14 + r
= 21 + r
Sin 30 = r /(21 + r)
=> 1/2 = r/(21 + r)
=> 21 + r = 2r
=> r = 21
Radius of larger sphere = 21 cm
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