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For a party, three solid cheese (OG2016)

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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For a party, three solid cheese (OG2016)

Post Fri May 06, 2016 12:29 pm
For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is (4/3)(pi)r^3, where r is the radius.)

A) 12
B) 16
C) cuberoot16
D) 3(cuberoot8)
E) 2(cuberoot36)

OA: E

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Post Wed May 11, 2016 11:56 pm
This seems too whimsical for the actual test - mashing three cheese balls together seems beneath the people at GMAC - but I'm glad to see it!

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Post Mon May 09, 2016 10:44 am
boomgoesthegmat wrote:
For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is (4/3)(pi)r^3, where r is the radius.)

A) 12
B) 16
C) cuberoot16
D) 3(cuberoot8)
E) 2(cuberoot36)

OA: E
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

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Post Wed May 11, 2016 11:56 pm
This seems too whimsical for the actual test - mashing three cheese balls together seems beneath the people at GMAC - but I'm glad to see it!

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