radius

[trim scaffold]

#1015578016606343218

[craggy zephyr]

What is the formula for volume of a hemisphere?

Remember it is 1/2 of a sphere

[nimble falcon]

Just remember that the water will cover same volume in cone as its in hemisphere
So calculate volume that water is taking in hemisphere which is two fifth volume of hemisphere
Then that will be equal to volume of water taking in cone. Take height h=12
Put both equal and solve for variable r

[trim scaffold]

hi guys i still not sure how to do it

[nimble falcon]

Think about this as this take some water in a bowl then transfer it to a glass. The quantity of water will be same no?.Just that water is liquid so it get itself adjusted with the shape you put it in.
Thats the concept here. And its taking same space(volume) in bowl or in glass.

[nimble falcon]

Now read this again try it

[trim scaffold]

so i do volume of shepre divide by 2/5

[nimble falcon]

No hemisphere which is half of sphere
Half of volume of sphere multiply by two fifth = volume of cone with h = 12

[trim scaffold]

i do the formula for the shepe divided by 2

sorry i not really good at maths

[nimble falcon]

Yeah divide by 2 or multiply by 1/2 same thing

It would give you formula of hemisphere 2/3 pie r^3

[trim scaffold]

then what do i do

[craggy zephyr]

Firstly what is the volume of the hemisphere?

@trim scaffold

[trim scaffold]

Is it 2 3 pi r 3

[craggy zephyr]

2/3 pi r^3

Yes

So r = 6

Solve for volume

[trim scaffold]

452.38

[craggy zephyr]

In terms of pi

[trim scaffold]

144

[craggy zephyr]

Ok what is 2/5 of that

Since that is the volume of the water

[trim scaffold]

28.8

[craggy zephyr]

That is 1/5

[trim scaffold]

57.6

[craggy zephyr]

Ok the depth of the water in the cone is the height of it

We need to find radius and we know area and height

We have 1/3 pi r^2 * h = A

1/3 * pi r ^2 * 12 = 57.6 pi

Solve for r

[trim scaffold]

So area is 57.6pi and height is 12cm so do I times them together

[craggy zephyr]

No

[craggy zephyr]

This

Divide pi from both sides to get rid of it

Then solve for

r

[trim scaffold]

Is this what I do to find the radius

[craggy zephyr]

No

Dividing pi from both sides we have

1/3 * r^2 * 12 = 57.6

4 * r^2 = 57.6

And so on

[trim scaffold]

So 12 divide pi

And 57.6 divide pi

[craggy zephyr]

?

No divide both sides by pi

Because that makes both sides still equal

And also cancels out the pi

And makes it multiplied by 1