Quantitative - Mathematics - Solid Geometry:

Three D Boxes

MCQ - 112-11964

Question:

A cube with volume 27 cubic inches is inscribed inside a sphere such that each vertex of the cube touches the sphere. What is the radius, in inches, of the sphere?

(3√3)/2 (approximately 2.60)
√3/2 (approximately 1.73)
8.5
√3/2 (approximately 1.73)

Correct Answer: A

Explanation:

We know that the cube has a volume of 27 cubic inches, so each side of the cube must be ∛27=3 inches. Since the cube is inscribed inside the sphere, the diameter of the sphere is the diagonal length of the cube, so the radius of the sphere is half of the diagonal length of the cube. To find the diagonal length of the cube, we use the distance formula d=√(32+32+32 )=√(3*32 )=3√3, and then divide the result by 2 to find the radius of the sphere, (3√3)/2.

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131 MCQ for effective preparation of the test of Three D Boxes of Solid Geometry section.

Read the MCQ statement: A cube with volume 27 cubic inches is inscribed inside a sphere such that each vertex of the cube touches the sphere. What is the radius, in inches, of the sphere?, keenly and apply the method you have learn through the video lessons for Three D Boxes to give the answer. Record your answer and check its correct answer and video explanation for MCQ No. 112-11964.

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Solve the question for MCQ No. and decide which option (A through D/E) is the best choice to answer the MCQ, then click/tap the blue button to view the correct answer and it explanation.

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