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For a party, three solid cheese (OG2016)

This topic has 2 expert replies and 1 member reply
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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    OptimusPrep Master | Next Rank: 500 Posts
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    Post Sat May 07, 2016 8:00 pm
    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
    r1 = 1,
    r2 = 2,
    r3 = 3.

    Volume of sphere = (4/3)πr^3

    V1 = (4/3)π
    V2 = (4/3)π*8
    V3 = (4/3)π*27

    Total Volume of the final sphere= (4/3)π*36
    Hence the radius = cuberoot(36)

    Diameter = 2*cuberoot(36)

    Correct Option: E

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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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