Question

A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hemisphere is modeled by the function V = 2/3 πr 3

Write a model for the radius as a function of the volume.
The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for π

Answer 1

You would need to invert your equation. IE solve for r. So we need everything at the end to equal r. Do you need help?

Answer 2

Yes, major help, I am new to this.

Answer 3

OK our equation is V=2/3 (pi)(r^3) Correct?

Answer 4

correct

Answer 5

I'm sorry the right side of the equation?

Answer 6

right side of the equation???

Answer 7

Never mind we need to reflect the answer with pi.

Answer 8

V=2/3 (pi)(r^3) So we need to move things from the right side to the left. To get rid of 2/3 from the right side what would we have to do to both sides of the equation?

Answer 9

Multiply

Answer 10

BY what?

Answer 11

3?

Answer 12

3 times 2/3 = 6/3 = 2. We need to get to 1. So 3 is incorrect. What would you multiply by 2/3 to get 1?

Answer 13

3/2

Answer 14

Correct so if we multiply both sides by 3/2 waht will our equation look like?

Answer 15

pi(r^3)

Answer 16

Actually \[\frac{ 3}{ 2 }V= \pi (r ^{3})\] What ever we do to one side we must do to the other. Now how do we make (pi) equal 1?

Answer 17

multiply 3/2 x 2/3

Answer 18

How do you make (pi) = 1. If 1 = pi/pi.

Answer 19

I'm guessing divide pi by pi?

Answer 20

Any value multiplied by its reciprocal will equal 1. Examble attached\[2 \times \frac{ 1 }{ 2 }=1.....or.....3\times \frac{ 1 }{ 3 }=1\] So (pi) x what = 1

Answer 21

(pi) times what will equal 1?

Answer 22

I don't know

Answer 23

The reciprocal of (pi) is 1/(pi)...\[\frac{ \pi }{ 1 }\times \frac{ 1 }{ \pi }= \frac{ \pi }{ \pi }..which equals..1\] Do you see this?

Answer 24

(pi) over one is the same as (pi)

Answer 25

ok

Answer 26

what does frac means

Answer 27

?

Answer 28

Now what does the equation look like when you multiply both sides by (pi)/1. Remember what ever you do to one side you must do to the other.

Answer 29

''[\frac{ \pi }{ 1 }\times \frac''

Answer 30

It was the equation (pi)/1 times 1/(pi) =1 but it must not have converted on your screen

Answer 31

ok cause how it was written out I never seen it written like that before

Answer 32

Now what does the equation look like when you multiply both sides by (pi)/1. Remember what ever you do to one side you must do to the other.