A sphere has a volume of 5.2 cubic inches. If the sphere's volume can vary between 4.4 cubic inches and 6.1 cubic inches , how can the radius vary? Round your answer to five decimal places.
A) Radius can vary between 1.01653 inches and 1.13348 inches.
B) Radius can vary between 1.61365 inches and 1.79929 inches.
C) Radius can vary between 0.27474 inch and 1.97474 inches.
D) Radius can vary between 1.85897 inches and 2.18882 inches.
E) Radius can vary between 1.02490 inches and 1.20676 inches.

Question

Quizplus · Accepted Answer

The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. To find the radius for the given volumes, we rearrange the formula to solve for $r$: $r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$. Plugging in the minimum volume (4.4 cubic inches) and the maximum volume (6.1 cubic inches) into this formula and solving for $r$ gives the range of the radius. Calculating these values gives a radius range approximately between 1.01653 inches and 1.13348 inches, which matches option A.

A Sphere Has a Volume of 5