Stuck on Maths Question

cb7

Can anyone help!!!!
This is the question I am stuck on.

A sphere of radius r cm is totally immersed in a water which is in a cylindrical can of radius 4cm. When the sphere is removed the water level drops by 1cm.

Find the radius of the sphere.
Have a picture just showing sphere in a cylindrical can with water (the water level is not specified).
Thanks

seklly

It's been a while since I've done Junior Cert Maths but I'd say you need to calculate the volume of the fluid displaced. i.e. the volume of the cylinder of 1 cm height and 4cm radius.

As this volume also equals the volume of the sphere, you put that into your volume of a sphere equation and solve for r.

spurious

The volume of the sphere is the same as a cylinder with radius 4cm and height 1cm.

Volume of a cylinder = pi r squared by the height.

Work out that volume (of the cylinder of water displaced) and then use that to work out the radius of the sphere.

Volume of a sphere = 4/3 pi r cubed.

Hope that makes sense.

hearny

seklly wrote: »

It's been a while since I've done Junior Cert Maths but I'd say you need to calculate the volume of the fluid displaced. i.e. the volume of the cylinder of 1 cm height and 4cm radius.

As this volume also equals the volume of the sphere, you put that into your volume of a sphere equation and solve for r.

It's been a while for me too with the maths but the sphere will displace its exact volume in water (Boyles law). So the volume of the sphere is exactly what was said above a cylinder of 1cm height and radius of 4 cm. (pii x r squared x h)

Can't remember the volume of a sphere formula.

Bedshaped

Since the water is in a cylindrical can we can imagine that any drop or rise in the level of the water can be an imaginary cylinder with height (h) of the difference in water level.

This is given by (volume of a cylinder)

If you take out the sphere the change in the volume of water must equal the volume of the sphere.

You calculate the volume of the cylinder of lost water using where h = 1 cm and then substitute that back in for the volume of a sphere formula where

Remember that

cb7

Thanks a million

I got
r^3 = 12

How do I get rid of the to ^3?

hearny

hearny wrote: »

It's been a while for me too with the maths but the sphere will displace its exact volume in water (Boyles law). So the volume of the sphere is exactly what was said above a cylinder of 1cm height and radius of 4 cm. (pii x r squared x h)

Can't remember the volume of a sphere formula.

Ignore me I'm too slow typing on the phone.

Donnielighto

hearny wrote: »

It's been a while for me too with the maths but the sphere will displace its exact volume in water (Boyles law). So the volume of the sphere is exactly what was said above a cylinder of 1cm height and radius of 4 cm. (pii x r squared x h)

Can't remember the volume of a sphere formula.

Archimedes law?

spurious

cb7 wrote: »

Thanks a million

I got
r^3 = 12

How do I get rid of the to ^3?

In my day we used log tables to get cube roots - there's probably something on a calculator, I don't know.

cb7

Thanks

cb7

One more question!!!

Solve 36^x + 2 = 216/√6

I got -2 but not sure if its right
Thanks