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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?

THE ANSWER IS 2BECAUSE..... 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.


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