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Question
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
Solution
Let r be the radius of the sphere.
Surface area = 4πr2 and volume = `4/3pir^3`
According to the condition:
`4pir^2 = 4/3pir^3`
`=> r^3/r^2 = 4pi xx 3/(4pi)`
`=>` r = 3 cm
Diameter of sphere = 2 × 3 cm = 6 cm
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