Mathematics, 13.12.2020 22:00 girlhooper4life11

• When volleyballs are purchased, they are not fully inflated. A partially inflated volleyball can be modeled by a sphere whose volume is approximately 180 in). After
being fully inflated, its volume is approximately 294 in. To the nearest tenth of an
inch, how much does the radius increase when the volleyball is fully inflated?

Answers: 3

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Answer from: caleelwittmann31

The radius increase when the volleyball is fully inflated is 0.5

Step-by-step explanation:

Volume of Partially inflated volleyball = 180 in³

Volume of Full inflated volleyball = 294 in³

We need to find how much does the radius increase when the volleyball is fully inflated?

First we will find the radius of both Partially inflated and Full inflated volleyball. Then we will find increase in radius.

The formula for Volume of sphere is: $Volume=\frac{4}{3}\pi r^3$

Finding Radius of Partially inflated volleyball

Volume = 180

Putting values and finding radius of Partially inflated volleyball

$Volume=\frac{4}{3}\pi r^3\\180=\frac{4}{3}*3.14*r^3\\4.186r^3=180\\r^3=\frac{180}{4.186}\\r^3=43.0\\Taking\:cube\:root\:on\:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{47}\\r= 3.6$

So, radius of Partially inflated volleyball is r = 3.6

Finding Radius of Fully inflated volleyball

Volume = 294

Putting values and finding radius of Fully inflated volleyball

$Volume=\frac{4}{3}\pi r^3\\294=\frac{4}{3}*3.14*r^3\\4.186\:r^3=294\\r^3=\frac{294}{4.186}\\r^3=70.23\\Taking\:cube\:root\:on\:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{70.23}\\r= 4.1$

So, radius of Partially inflated volleyball is r = 4.1

Now, finding increase in radius by subtracting radius of fully inflated volleyball with partially inflated volleyball

Increase in radius of Fully inflated volleyball = 4.1 - 3.6

Increase in radius of Fully inflated volleyball = 0.5

So, the radius increase when the volleyball is fully inflated is 0.5

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

ok so what's the question?

step-by-step explanation:

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