Question: A globe of radius 8 inches is to be placed into a square box for shipment. The globe’s stand will be in a separate container. What is the minimum inside volume that the box can be? (The formula for the volume of a sphere is 4πr^3.)
(A) 32π cubic inches.
(B) 512π cubic inches.
(C) 2,048π cubic inches.
(D) 4,096π cubic inches.
(E) 4,096 cubic inches.
“A globe of radius 8 inches is to be placed into a square box for shipment''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section measures the candidates’ agility in analysing the quantitative problems and solving them with the proper mathematical calculations. The candidates must choose the valid option by calculating the entire sum properly and logically. The candidates should have knowledge of mathematics regarding algebra, arithmetic and geometry in order to crack GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part demonstrates mathematical problems to be deciphered with proper quantitative knowledge.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that
Given:
- A globe of radius 8 inches is placed into a square box
Find out:
- The minimum inside volume of the box
A globe is placed into a square box, therefore the box is in the shape of a cube.
Therefore, the diameter of the globe can be considered as each side of a cube.
The radius of the globe is 8 inches as given in the question
Therefore, the diameter of the globe= 16 inches ( since, diameter of sphere = 2* radius)
Hence we can infer that each side of the cube= 16 inches
Therefore, the minimum inside volume of the box = 16* 16 * 16 (since, volume of the cube = side^3)
= 4096 cubic inches
Correct Answer: (E)
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