ISEE Upper Level Quantitative : Spheres

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

Example Question #43 : Solid Geometry

 is a positive number. Which is the greater quantity?

(A) The surface area of a sphere with radius 

(B) The surface area of a cube with edges of length 

Possible Answers:

(A) is greater

(A) and (B) are equal 

It is impossible to determine which is greater from the information given

(B) is greater

Correct answer:

(B) is greater

Explanation:

The surface area of a sphere is  times the square of its radius, which here is ; the surface area of the sphere in (A) is .

The area of one face of a cube is the square of the length of an edge, which here is , so the area of one face of the cube in (B) is . The cube has six faces so the total surface area is .

, so , giving the sphere less surface area. (B) is greater.

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