Question

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

Answer 1

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.

Answer 2

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 \[V=\frac{ 4 }{ 3 } \Pi (70)^3\]

Answer 3

Is this correct so far?

Answer 4

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?

Answer 5

Or would it be

\[V=\frac{ 4 }{ 3}(\Pi 70^3)\]

Answer 6

Oh I see. Hang on a sec

Answer 7

(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)

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

Do you have a calculator?

Answer 15

Yes but I have to show all work.

Answer 16

You have to show the multiplication and division?

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

That is rounded to the nearest whole number

Answer 22

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

Answer 23

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

Answer 24

Thank you

Answer 25

yw