Unofficialllyy
  • Unofficialllyy
Can someone help with this geometry problem? I will fan and medal!
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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Unofficialllyy
  • 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
  • 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
  • Unofficialllyy
Is this correct so far?

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Vocaloid
  • 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
  • Unofficialllyy
Or would it be \[V=\frac{ 4 }{ 3}(\Pi 70^3)\]
Unofficialllyy
  • Unofficialllyy
Oh I see. Hang on a sec
Vocaloid
  • 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
  • Unofficialllyy
I'm not sure, when I watched the help video it said to use the formula for the volume of a sphere.
Vocaloid
  • Vocaloid
volume of a quarter-sphere = (1/4)*volume of sphere
Mertsj
  • 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
  • Unofficialllyy
So I find the volume first then multiply it by 1/4?
Mertsj
  • Mertsj
yes, that will work. Or as I have shown you could multiply 70^3 by pi and divide by 3
Unofficialllyy
  • Unofficialllyy
i am stuck on the \[V=\frac{ 4 }{ 3 } \pi (70)^3\] part though. Like how do I go about solving this?
Mertsj
  • Mertsj
Do you have a calculator?
Unofficialllyy
  • Unofficialllyy
Yes but I have to show all work.
Mertsj
  • Mertsj
You have to show the multiplication and division?
Unofficialllyy
  • Unofficialllyy
I dont think so, just explain what I did. But yes I have a calculator
Mertsj
  • Mertsj
Then put these steps on your paper: Volume of 1/4 sphere = 1/4 x 4/3 x pi x r^3
Mertsj
  • Mertsj
Now cancel the fours and substitute 70 for r and write: V = 1/3 x 3.14 x 70x70 x 70
Unofficialllyy
  • Unofficialllyy
I think I got the answer. Is this right? \[V=359189\]
Unofficialllyy
  • Unofficialllyy
That is rounded to the nearest whole number
Mertsj
  • Mertsj
Now do 70 x 70 x 70 on your calculator and write: V = 1/3 x 3.14 x 343,000
Mertsj
  • Mertsj
Now multiply that by 3.14 and divide by 3 and write: V = 359007 ft^3
Unofficialllyy
  • Unofficialllyy
Thank you
Mertsj
  • Mertsj
yw

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