Question

if the radius of a sphere is 3 cm, what is its volume?
a. 36π
b. 36\frac{π}{3}
c. 18π
d. 81π
if a sphere has a diameter of 14 inches, what is its radius?
a. 7 inches
b. 28 inches
c. 14 inches
d. 21 inches

Explanation:

First Question:

Step1: Recall the volume formula for a sphere

The volume $$V$$ of a sphere is given by the formula $$V=\frac{4}{3}\pi r^{3}$$, where $$r$$ is the radius of the sphere.

Step2: Substitute the given radius into the formula

Given $$r = 3$$ cm. Substitute into the formula: $$V=\frac{4}{3}\pi(3)^{3}$$.
First, calculate $$(3)^{3}=3\times3\times3 = 27$$. Then, $$\frac{4}{3}\times27=36$$. So, $$V = 36\pi$$ cm³.

Second Question:

Step1: Recall the relationship between radius and diameter

The radius $$r$$ of a circle (or sphere) is related to the diameter $$d$$ by the formula $$r=\frac{d}{2}$$.

Step2: Substitute the given diameter into the formula

Given $$d = 14$$ inches. Substitute into the formula: $$r=\frac{14}{2}=7$$ inches.

Answer:

1. A. \(36\pi\)
2. A. 7 inches