Can someone help with this geometry problem? I will fan and medal!

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- Unofficialllyy

Can someone help with this geometry problem? I will fan and medal!

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

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- Unofficialllyy

The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.

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- Unofficialllyy

I know I have to use the formula for volume of a sphere which is \[V=\frac{ 4 }{ 3 } \Pi r^3\]
Then I plug in 70 to get \[V=\frac{ 4 }{ 3 } \Pi (70)^3\]

- Unofficialllyy

Is this correct so far?

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## More answers

- Vocaloid

well, yes, you are correct so far
V is the volume of the entire sphere, so how do we find the volume of a quarter sphere?

- Unofficialllyy

Or would it be
\[V=\frac{ 4 }{ 3}(\Pi 70^3)\]

- Unofficialllyy

Oh I see. Hang on a sec

- Vocaloid

(as a side note, V = (4/3)(pi*70^3) is the same as V = (4/3)(pi)(70^3) because of order of operations)

- Unofficialllyy

I'm not sure, when I watched the help video it said to use the formula for the volume of a sphere.

- Vocaloid

volume of a quarter-sphere = (1/4)*volume of sphere

- Mertsj

Volume of sphere:
\[\frac{4}{3}\pi r^3\]
Volume of 1 quarter of sphere:
\[\frac{1}{4}\times\frac{4}{3}\pi r^3=\frac{1}{3} \pi r^3\]

- Unofficialllyy

So I find the volume first then multiply it by 1/4?

- Mertsj

yes, that will work. Or as I have shown you could multiply 70^3 by pi and divide by 3

- Unofficialllyy

i am stuck on the \[V=\frac{ 4 }{ 3 } \pi (70)^3\] part though. Like how do I go about solving this?

- Mertsj

Do you have a calculator?

- Unofficialllyy

Yes but I have to show all work.

- Mertsj

You have to show the multiplication and division?

- Unofficialllyy

I dont think so, just explain what I did. But yes I have a calculator

- Mertsj

Then put these steps on your paper:
Volume of 1/4 sphere = 1/4 x 4/3 x pi x r^3

- Mertsj

Now cancel the fours and substitute 70 for r and write:
V = 1/3 x 3.14 x 70x70 x 70

- Unofficialllyy

I think I got the answer. Is this right?
\[V=359189\]

- Unofficialllyy

That is rounded to the nearest whole number

- Mertsj

Now do 70 x 70 x 70 on your calculator and write:
V = 1/3 x 3.14 x 343,000

- Mertsj

Now multiply that by 3.14 and divide by 3 and write:
V = 359007 ft^3

- Unofficialllyy

Thank you

- Mertsj

yw

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