Anyone ready for a math question.
For a question like this, I like to plug in a random number, do the suggestion, and then observe the end result.
I did this question before, but I forgot the answer.
Just use formula: it is known that \(V = \dfrac{4}{3}\pi r^3\) and \(SA = 4\pi r^2\) Just plug 1/4 r in r, then simplify it
replace r to 1/4 r
OKay, give me a minute to get the answer.
The volume of a sphere is V=(4/3)Πr². Let's plug in 4 to make it easy. You get 66.99 as your volume. Do you follow it so far?
I got (pi)/12
Now, multiply 4 by 1/4. You get 1. When you plug it back in, you get 4.19.
1
You multiplied 16 (r²) by 3/4, not 4/3. If you multiply it by 4/3, you get 21.33.
I thought for volume I use 4/3?
You do. You multiplied it by 3/4 though.
What would be r?
\[V = \dfrac{3}{4}\pi r^3\]Plug in \(\dfrac{1}{4}\); \[\large V_{new} = \dfrac{3}{4}\pi \left(\dfrac{1}{4}r\right)^3 = \left(\dfrac{1}{4}\right)^3\left(\dfrac{3}{4}\pi r^3\right) = \left(\dfrac{1}{4}\right)^3(V)\]Do you know what (1/4)^3 is?
Plug in \(\dfrac{1}{4}r\) **
1/64
Yes, so \(\Large V_{new} = \dfrac{1}{64}V\) So that means volume is multiplied by 1/64 does that make sense?
So the volume is 1/64 and the surface area is 1/16?
Yes
you squared 1/4 in surface area, so you will get 1/16.
Alright, thank you so much. Do you have time for another question?
Yes of course
I'll post a as a new question. I'll tag you.
alright
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