https://web2.0calc.com/questions/help_98409

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Guest May 19, 2020

#1**+1 **

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)

CPhill May 19, 2020

#2**+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

CPhill May 19, 2020