Bunuel wrote:
Q is a cube. Find the volume of the cube.
(1) The total surface area of Q is 150 sq cm
(2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION:Another simple prompt, and again, we need the volume.
Statement #1 tells us surface area is 150. Well, for a cube, SA = 6s^2. If we know 150 = 6s^2, we can solve for s, which will allow us to calculate the volume. Statement #1 is by itself sufficient.
Statement #2 tell us the space diagonal has a length of \(5*\sqrt{3}\). Well, the three-dimensional version of the Pythagorean Theorem tell us that:
\((5*\sqrt{3})^2 = s^2 + s^2 + s^2\)
That would allow us to solve for s, which would allow us to calculate the volume. Statement #2 is by itself sufficient.
Both statements sufficient by themselves. Answer = D.
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