An automatic ice-cream scoop serves spherical helpings of ice cream. The scoop can be adjusted to serve helpings from 1 inch in diameter to 2 inches in diameter. If Tim orders a scoop with a 2-inch diameter, and if Paul wants only half as much ice cream?

Answer 1

THE ANSWER IS 2

BECAUSE..... We have to use Tim's scoop radius to calculate his scoop volume, then divide it by 2 to find Paul's scoop volume and finally calculate its radius to get the diameter. Tim's scoop radius is diameter/2= 2 inch/2= 1 inch. So, the formula for Tim's scoop volume, i.e. volume of a sphere is 4/3*pi*(radius cubed)= 4/3*pi, because the radius 1 inch cubed is also 1. Now, Paul's scoop volume is half of Tim's, i.e. (4/3*pi)*1/2= 4/6*pi. Then, we equate this value with the formula for volume of a sphere to find Paul's scoop radius, and multiply by 2 to get the diameter, which is 2*(cube root of 1/2). I hope I said it right! ADDITIONAL DETAILS: After finding Paul's scoop volume(4/6*pi), you have to write, 4/3*pi* radius cubed= 4/6*pi(i.e. Paul's scoop volume and the volume of a sphere are the same thing, because the scoop is a sphere, isn't it?) then you can cancel out 4/3 and pi from both sides(as you should know, similar quantities can be cancelled from both sides of an equation- if both the quantities are in multiplied or divided form). That's where pi goes, and 4/3 too, and you have: radius cubed= 1/2; therefore, radius= cube root of 1/2. Hence, diameter= 2*cube root of 1/2. If you still have problems, feel free to say it.