Question

what is the volume of the cylinder? use 3.14 for $\pi$.
$v = \frac{4}{3}\pi r^3$ formula for volume of a sphere
$= \frac{4}{3}\pi(6)^3$ the diameter of the ball is 12 centimeters, so the radius is $12 \div 2 = 6$ centimeters.
$= 288\pi$
$\approx 904.32\\ \text{cm}^3$
the volume of the ball is about 904.32 cubic centimeters.

marcus is using small stone spheres as garden decorations. what is the volume of the stone sphere at the right? use 3.14 for $\pi$.

1. what is the radius of the stone sphere?

1. what is the volume of the stone sphere?

$v = \frac{4}{3}\pi r^3$
$= \frac{4}{3}\pi(\square)^3$
$= \frac{4}{3}\pi(\square)$
$= \square\\ \pi$
$\approx \square\\ \text{in.}^3$

1. another stone sphere for the garden has a diameter of 10 inches. what is the volume of this stone? use 3.14 for $\pi$, and round to the nearest hundredth.

Explanation:

Step1: Find the radius of the stone sphere in question 1

The formula for the radius \(r\) of a sphere when given the diameter \(d\) is \(r=\frac{d}{2}\). But in the second problem (the one with the sphere in the image), the radius is directly given as \(r = 6\) inches.

Step2: Calculate the volume of the stone sphere in question 2

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\).
Substitute \(r = 6\) into the formula:
\(V=\frac{4}{3}\pi(6)^{3}\)
First, calculate \(6^{3}=6\times6\times6 = 216\).
Then, \(\frac{4}{3}\times216=288\). So \(V = 288\pi\).
Using \(\pi=3.14\), \(V=288\times3.14=904.32\) \(in^{3}\)

Step3: Calculate the volume of the sphere in question 3

Given \(d = 10\) inches, find \(r=\frac{d}{2}=\frac{10}{2}=5\) inches.
Use the volume formula \(V=\frac{4}{3}\pi r^{3}\).
Substitute \(r = 5\) into the formula: \(V=\frac{4}{3}\pi(5)^{3}\)
Calculate \(5^{3}=5\times5\times5 = 125\).
Then, \(\frac{4}{3}\times125=\frac{500}{3}\). So \(V=\frac{500}{3}\pi\).
Using \(\pi = 3.14\), \(V=\frac{500}{3}\times3.14=\frac{1570}{3}\approx523.33\) \(in^{3}\)

Answer:

1. \(6\) inches
2. \(V=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi(216)=288\pi\approx904.32\) \(in^{3}\)
3. \(523.33\) \(in^{3}\)