PSAT Math Multiple-Choice Question 796: Answer and Explanation

Question: 796

Which of the following expressions is equivalent to the diameter of the sphere portrayed above, with a radius of r and volume V?

• A. 2
• B. πr3
• C.
• D.

Correct Answer: A

Explanation:

(A) The volume of a sphere is given by the formula V = πr³. The diameter is twice the radius, so we can solve for the radius and multiply by 2. To solve for r, first divide both sides by π:

To solve for r, take the cube root of both sides:
= r
Multiply this by 2 to get an expression for the diameter:
d = 2
Choice (A) is the correct answer.