The volume of a sphere is 70 cm3 correct to the nearest cm3 . Calculate the upper bound for the surface area of the sphere. Give your answer correct to 1 decimal place. You must show all your working.

where ( r ) is the radius of the sphere. Given that the volume ( V ) is 70 cm³ (correct to the nearest cm³), we can calculate the radius using the formula above:

r=(3V4π)1/3

r=(4π3V)1/3

Substituting ( V = 70 ) cm³ into the equation gives us the radius ( r ). However, since the volume is given correct to the nearest cm³, the actual volume could be anywhere from 69.5 cm³ to 70.5 cm³. Therefore, the upper bound for the radius ( r ) would be calculated using ( V = 70.5 ) cm³.

The surface area of a sphere is given by the formula:

A=4πr2

We can substitute the upper bound of ( r ) into this formula to get the upper bound for the surface area of the sphere.

Swap sides so that all variable terms are on the left hand side.

43πr3=V

Divide both sides by 43π.

43π43πr3=43πV

Dividing by 43π undoes the multiplication by 43π.

r3=43πV

Solve for V

V=43πr3