Problem

Solve for the specified variable. See Example 8. …

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Problem 32 Medium Difficulty

See Examples $5-7 .$ If you do not have a calculator, use 3.14 as an approximation of $\pi .$ Answers may vary slightly depending on which approximation of $\pi$ is used.
Rubber Bands. The world's largest rubber band ball is $5 \frac{1}{2} \mathrm{ft}$ tall and was made in 2006 by Steve Milton of Eugene, Oregon. Find the volume of the ball. Round to the nearest cubic foot. Hint: The formula for the volume of a sphere is $\left.V=\frac{4}{3} \pi r^{3} .\right)(\text { Source: timesunion.com })$

Answer

Volume of ball is 87.148 cubic feet

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 4

Formulas

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Video Transcript

and this problem, we're told. The world's largest rubber band ball is 5.5 feet tall. So essentially we have a sphere, and we know that the height of the sphere is 5.5 feet. And what we're being asked for is to find the vault. Now, if you know this, your directions tell you the formula to find the volume of a sphere. It's V equals 4/3 pi are cute. Well, because we're being asked the volume, we must know what the radius is. Well, because we're talking about a sphere, the length across of it would really represent a diameter. So this 5.5 fi represents the diameter of this fear. Well, we don't need the diameter. We need the radius. But remember, the radius is half of the diameter. So to find the radius, we simply take the diameter, which is 5.5 and divided by two, which will give us 2.75 feet. Now we simply need to substitute 2.75 feet in for R and R Formula in order to find the volume. So we're gonna have V equals 4/3 times pi times 2.75 So the third. Now we can go ahead and solve this. Well, first, we need to raise 2.75 to the third power, which will give us 4/3 pi times 20 0.796875 Now what I can do is multiply this by 4/3 so I'm gonna multiply 4/3 times 20.796875 And that's going to give me 27.72916667 times pi. Now, if your calculator has pie, which mine does, I'm just going to use the pie button. If you calculate it does not have pie, then you simply need toe multiplied this value by 3.14 And when I do this, I'm going to get 87 0.1137 462 nights. Now let's go back to our directions. They want us around to nearest cubic foot, meaning to the nearest hole number. So we look at the Temps place, which is of one, and because it's less than five, it's not going to change. Our seven is going to stay as it's so in other words with found the volume to be 87. Now we're going to use units. Remember, The units for volume is always cute while our diameter was in terms of feet. So our units for our volume will be feet cute.

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