Question

find the volume of a sphere with a radius of 1. round your answer to the nearest hundredth if necessary. show your work here hint: to add the pi symbol (π), type \pi\

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume \( V \) of a sphere with radius \( r \) is \( V=\frac{4}{3}\pi r^{3} \).

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 1 \). Substituting \( r = 1 \) into the formula, we get \( V=\frac{4}{3}\pi(1)^{3} \). Since \( 1^{3}=1 \), this simplifies to \( V = \frac{4}{3}\pi \).

Step3: Calculate the numerical value (if needed)

If we use the approximation \( \pi\approx3.14159 \), then \( V=\frac{4}{3}\times3.14159\approx4.18879 \). Rounding to the nearest hundredth, we get \( V\approx4.19 \).

Answer:

The volume of the sphere is \(\frac{4}{3}\pi\) (or approximately \(4.19\) when rounded to the nearest hundredth).