The surface area of a sphere is `346.5` `cm^2`, calculate its radius and the volume.

Explanation

Let the radius of the sphere be `r cm.`
Then, its surface area `= (4pi r^(2)) cm^(2)`
`:. 4pir^(2) = 346.5 rArr 4 xx (22)/(7) xx r^(2) = 346.5`
`rArr r^(2) = (346.5 xx (7)/(88)) = ((3465 xx 7)/(10 xx 88)) = (441)/(16)`
`rArr r = (21)/(4) = 5.25`
Thus, the radius of the sphere is `5.25 cm.`
Volume of the sphere `= ((4)/(3) pi r^(3)) cm^(2)`
`= ((4)/(3) xx (22)/(7) xx 5.25 xx 5.25 xx 5.25) cm^(3)`
`= ((4)/(3) xx (22)/(7) xx (525)/(100) xx (525)/(100) xx (525)/(100)) cm^(3)`
`= (4851)/(8) cm^(3) = 606.375 cm^(3)`
Hence, the volume of the sphere is `606.375 cm^(3)`