Last Updated on May 10, 2023
GMAT Guide
Solution:
We first need to determine the volume of each individual cheese ball. We have 3 cheese balls of diameters of 2, 4, and 6 inches, respectively. Therefore, their radii are 1, 2 and 3 inches, respectively. Now let’s calculate the volume for each cheese ball.
Volume for 2-inch diameter cheese ball
(4/3)π(1)^3 = (4/3)π
Volume for 4-inch diameter cheese ball
(4/3)π(2)^3 = (4/3)π(8) = (32/3)π
Volume for 6-inch diameter cheese ball
(4/3)π(3)^3 = (4/3)π(27) = (108/3)π
Thus, the total volume of the large cheese ball is:
(4/3)π + (32/3)π + (108/3)π = (144/3)π = 48π
We can now use the volume formula to first determine the radius, and then the diameter, of the combined cheese ball.
48π = 4/3π(r)^3
48 x 3 = 4(r)^3
144 = 4(r)^3
36 = r^3
r = (cube root)√36
Thus, the diameter = 2*(cube root)√36
Answer: E
