Help due today

1.In parallelogram ABCD, A = (4, 5), B = (1, 4), and C = (6, 2). Find the coordinates of D.

We  have  three possibilities  for  D

a)  ( 4 + 1  - 6, 5 + 4 - 2)   =   ( -1, 7)

b) ( 4 + 6 - 1, 5  + 2 - 4)  =   ( 9, 3)

c)  ( 1 + 6 - 4, 4 + 2 - 5)  =  ( 3, 1)

2.A right cylinder with a base radius of 3 units is inscribed in a sphere of radius 5 units. Find the total volume, in cubic units, of the space inside the sphere and outside the cylinder.

The  only tricky thing  is  finding (1/2)  the  height of the cylinder.....this  equals

sqrt  ( radius of sphere^2  -  radius of cylinder^2 )  =  sqrt (5^2 - 3^2)  = sqrt (16)  =  4

So

Volume of sphere  =  (4/3)pi (5)^3

Volume of cylinder  =  pi (3)^2 * 8

So  the volume we are looking for  is

(4/3) pi ( 5)^3  - pi (3^2) * 8   =

pi  [ ( 4/3)(125)  - (9)(8) ]   =

pi  [ 500/3  - 72 ]  =

pi  [ 500 -216] / 3   =

(284 / 3)  pi    units^3   ≈  297.4  units^3

And those other kids say their homework is hard and time-consuming. 

You have mastered the art of time and skill allocation. 

Clever you.