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04 Jul 2019, 06:08
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What is the volume of Cube A?
(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) square meters.
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\) meters.
(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) square meters.
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\) meters.
04 Jul 2019, 06:08
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Official Solution:
What is the volume of Cube A?
In answering this question, it's important to note that you don't need to perform any calculations or know specific formulas. In data sufficiency questions, it's sufficient to recognize that you can determine the value, rather than actually finding the value itself.
(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) square meters.
Knowing the surface area of an inscribed sphere, we can determine the sphere's diameter, which would be equal to the length of a side of the cube. This allows us to calculate the volume of the cube. Sufficient.
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\) meters.
Similarly, the diameter of the circumscribing sphere is equal to the length of a diagonal of the cube. This information allows us to determine the volume of the cube. Sufficient.
Answer: D
What is the volume of Cube A?
In answering this question, it's important to note that you don't need to perform any calculations or know specific formulas. In data sufficiency questions, it's sufficient to recognize that you can determine the value, rather than actually finding the value itself.
(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) square meters.
Knowing the surface area of an inscribed sphere, we can determine the sphere's diameter, which would be equal to the length of a side of the cube. This allows us to calculate the volume of the cube. Sufficient.
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\) meters.
Similarly, the diameter of the circumscribing sphere is equal to the length of a diagonal of the cube. This information allows us to determine the volume of the cube. Sufficient.
Answer: D
06 May 2023, 04:07
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
