A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places.
A) Radius can vary between 0.91416 inch and 1.09503 inches.
B) Radius can vary between 1.45113 inches and 1.73825 inches.
C) Radius can vary between 0.18475 inch and 2.48475 inches.
D) Radius can vary between 1.58533 inches and 2.07839 inches.
E) Radius can vary between 0.87404 inch and 1.14587 inches.

Question

A sphere has a volume of 4.0 cubic inches. If the sphere's volume can vary between 3.2 cubic inches and 5.5 cubic inches , how can the radius vary? Round your answer to five decimal places. ​
A) Radius can vary between 0.91416 inch and 1.09503 inches.
B) Radius can vary between 1.45113 inches and 1.73825 inches.
C) Radius can vary between 0.18475 inch and 2.48475 inches.
D) Radius can vary between 1.58533 inches and 2.07839 inches.
E) Radius can vary between 0.87404 inch and 1.14587 inches.

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 solve for $r$ in the volume formula. For the minimum volume of 3.2 cubic inches, $r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$, which gives a radius of approximately 0.91416 inches. For the maximum volume of 5.5 cubic inches, using the same formula, the radius is approximately 1.09503 inches.

A Sphere Has a Volume of 4