Question

Anyone ready for a math question.

Answer 1

For a question like this, I like to plug in a random number, do the suggestion, and then observe the end result.

Answer 2

I did this question before, but I forgot the answer.

Answer 3

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

Answer 4

replace r to 1/4 r

Answer 5

OKay, give me a minute to get the answer.

Answer 6

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?

Answer 7

I got (pi)/12

Answer 8

Now, multiply 4 by 1/4. You get 1. When you plug it back in, you get 4.19.

Answer 9

1

Answer 10

You multiplied 16 (r²) by 3/4, not 4/3. If you multiply it by 4/3, you get 21.33.

Answer 11

I thought for volume I use 4/3?

Answer 12

You do. You multiplied it by 3/4 though.

Answer 13

What would be r?

Answer 14

\[V = \dfrac{3}{4}\pi r^3\]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?

Answer 15

Plug in \(\dfrac{1}{4}r\) **

Answer 16

1/64

Answer 17

Yes, so \(\Large V_{new} = \dfrac{1}{64}V\)
So that means volume is multiplied by 1/64

does that make sense?

Answer 18

So the volume is 1/64 and the surface area is 1/16?

Answer 19

Yes

Answer 20

you squared 1/4 in surface area, so you will get 1/16.

Answer 21

Alright, thank you so much. Do you have time for another question?

Answer 22

Yes of course

Answer 23

I'll post a as a new question. I'll tag you.

Answer 24

alright

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Answer 43

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