A sphere with a 4-in radius is being plated with silver for a cost of $30.

Question

A sphere with a 4-in radius is being plated with silver for a cost of $30. To the nearest hundredth, what is the radius of a sphere which is plated with silver for a cost of $80?

Answer 1

The surface area of a sphere is 4*π*r². So the surface area of the first sphere is 4 * 4² * π = 64π in². Now that we know the surface area, we want to know what the price of silver is per inches squared. So take the price and divide it by the surface area. 30/(64π in²) = $15/(32π in²). Now that we know the price per in², let's figure out the surface area of a sphere the costs $80 to coat in silver. price * surface-area = total cost ==> $15/(32π in²) * surface-area = $80 ==> surface area = ($80/$15) * (32π in²) = (16/3) * (32π in²) = 512π in².

 

Okay, we're almost there! So we know that the surface area of this new sphere is 512π in². This means that 4 * π * (new radius)² in² = 512π * in². Dividing both sides by 4π in² what we get is ==> (new radius)² = 128 ==> (new radius) = sqrt(128) = 11.314.