Question

How to do questions a and b?

Answer 1

Below

Explanation:

1a) (i)

Surface Area of the cylinder
= Surface area of a sphere + Area of the side of the cylinder

Why is it the surface area of a sphere?
Well, the two hemispheres that are cut from the cylinder, they resemble a sphere when the two hemispheres are put together. Their combined surface area will equal to the surface area of a sphere.

For the side of the cylinder, it is actually a rectangle wrapped around the two circles as you can see from the cylinder cut out below

The length of the rectangle is basically the circumference of the circle and the width of the rectangle is actually the height of the cylinder.

So combining all of the above together, your surface area for your cylinder is `4pir^2+2pir*h=1000pi` which simplifies to `4pir^2+2pirh=1000pi`

1a) (ii) To find h in terms of r, you have to rearrange the equation to make h the subject

`4pir^2+2pirh=1000pi`
`2pirh=1000pi-4pir^2`
`h=1/(2pir)(1000pi-4pir^2)`
`h=((2pi)(500-2r^2))/(2pir)`
`h=(500-2r^2)/r`cm

1b) (i)
Volume of the cylinder:
=Volume of the cylinder - volume of the sphere
= `r^2pi*h-(4pir^3)/3`
= `r^2pi(h-(4r)/3)` `cm^3`