GMAT Math

Hi,
I was going through Manhattan GMAT geometry book - chapter 3, question 10 regarding rectangular box with the dimensions of 12 inch, 10 inch, 8 inch and is asked to find largest possible volume of right cylinder that is placed inside the box....

I referred to the answer explanation where in only three possibilities are considered... case 1: r=5 & h=8 ; case 2 : r=4 & h=10 ; case 3 : r=4 & h=12... why other possibilities are not considered such as case 4 : r=6 & h=10 ; case 5 : r=6 & h=8 ; case 6 r=5 & h=12.... If case 4,5 and 6 is considered answer changes to 360 TT

Because you cannot put cylinder r=6 into that box if r=6 diameter is 12
means box should be at least 12x12
Case 6 is similar if r=5 you have to use 12x10 side for cylinder base and height cannot be more than 8

JinalShah wrote:Hi,
I was going through Manhattan GMAT geometry book - chapter 3, question 10 regarding rectangular box with the dimensions of 12 inch, 10 inch, 8 inch and is asked to find largest possible volume of right cylinder that is placed inside the box....

I referred to the answer explanation where in only three possibilities are considered... case 1: r=5 & h=8 ; case 2 : r=4 & h=10 ; case 3 : r=4 & h=12... why other possibilities are not considered such as case 4 : r=6 & h=10 ; case 5 : r=6 & h=8 ; case 6 r=5 & h=12.... If case 4,5 and 6 is considered answer changes to 360 TT