## Unofficialllyy one year ago Can someone help with this geometry problem? I will fan and medal!

1. 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.

2. 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 $V=\frac{ 4 }{ 3 } \Pi (70)^3$

3. Unofficialllyy

Is this correct so far?

4. 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?

5. Unofficialllyy

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

6. Unofficialllyy

Oh I see. Hang on a sec

7. 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)

8. Unofficialllyy

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

9. Vocaloid

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

10. Mertsj

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

11. Unofficialllyy

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

12. Mertsj

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

13. Unofficialllyy

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

14. Mertsj

Do you have a calculator?

15. Unofficialllyy

Yes but I have to show all work.

16. Mertsj

You have to show the multiplication and division?

17. Unofficialllyy

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

18. Mertsj

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

19. Mertsj

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

20. Unofficialllyy

I think I got the answer. Is this right? $V=359189$

21. Unofficialllyy

That is rounded to the nearest whole number

22. Mertsj

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

23. Mertsj

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

24. Unofficialllyy

Thank you

25. Mertsj

yw