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24 Jan 2019, 04:53
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D
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85% (00:53) correct
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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.
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24 Jan 2019, 05:52
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Bunuel
#1
surface area of sphere = 4* pi * r^2
4* pi * r^2 = 100 pi
r = 5 ; d = 10 sqrt3
side of cube can be determined ; sufficient
digonal of cube = s sqrt3
#2
given diameter = 10 sqrt 3
radius 5 sqrt 3
sufficeint
IMO D
06 May 2023, 04:08
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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
