Question

1. a gumball shaped like a sphere has a radius of 12 millimeters. what is the volume of the gumball in cubic millimeters? round your answer to the nearest hundredth. type a response

Explanation:

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

We are given that the radius \( r = 12 \) millimeters. Substituting this into the formula, we get \( V=\frac{4}{3}\pi(12)^3 \).
First, calculate \( 12^3 = 12\times12\times12 = 1728 \).
Then, \( \frac{4}{3}\times1728 = 4\times576 = 2304 \).
So now the volume is \( V = 2304\pi \).

Step3: Calculate the numerical value and round

Using \( \pi\approx3.14159 \), we have \( V\approx2304\times3.14159 \).
\( 2304\times3.14159 = 2304\times3 + 2304\times0.14159 = 6912+326.22336 = 7238.22336 \).
Rounding to the nearest hundredth, we look at the thousandth place digit, which is 3. Since \( 3<5 \), we round down. So \( V\approx7238.22 \).

Answer:

7238.22