Radius of a sphere formed by the combination of three spheres of radius 3 cm, 4 cm and 5 cm, is .
A
27 cm
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B
64 cm
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C
6 cm
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D
12 cm
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Solution
The correct option is C 6 cm Let the radius of the larger sphere be R.
Given:
Radius of first sphere= r1=3cm
Radius of second sphere = r2=4cm
Radius of third sphere = r3=5cm
We know that when we combine many solids to form one solid, the volume remains same.
⇒ Volume of the larger sphere = Sum of volume of three spheres ⇒43πR3=43πr13+43πr23+43πr33 ⇒R3=r13+r23+r33 ⇒R3=33+43+53 ⇒R3=27+64+125 ⇒R3=216 ⇒R3=63 ⇒R = 6 cm