If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving

Question: If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

1. r = ½ e
2. r = e
3. r = 2e
4. r = √e
5. r = ¼ e^2

“If a sphere with radius r is inscribed in a cube with edges of length''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The GMAT quant section measures the candidates’ skills to evaluate the quantitative problems logically. The candidates must select the correct option by calculating the sum properly by following mathematical rules. The candidates should have basic maths concepts to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part presents calculative mathematical problems that can be solved with proper quantitative knowledge. The candidates can practice questions by answering from the book “Kaplan GMAT Math Workbook”.

Solution and Explanation:

There is only one solution to this problem.

Approach Solution 1:

The problem statement informs that:

Given:

• A sphere with radius r is inscribed in a cube with edges of length e

The question here asks to establish a relationship between r and e.

A sphere inscribed within a cube means the diameter of the sphere is equal to the side of the cube.
The radius of the sphere= r.
Then diameter = 2r.
Therefore, we can say, 2r = e (since it is given that e is the side of a cube)
In the next step, we can write, r= e/2
Therefore, r= ½ e

Correct Answer: (A)

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