Pls Help Due Tmrow

2)The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 150pi.

We have 

150 pi  =  pi [ 5/6 h ] ^2 * h         divide out pi

150  =  (25/36) h^3            multiply both sides by 36/25

150 (36/25)  = h^3

216  = h^3

6  =  h

So...r  = (5/6)h  = (5/6)(6)  = 5

So....the surface area  is

2pi * r  [ r + h ]  =

2pi * (5) [ 5 + 6 ] =

2pi * 55

110 pi  units^2

9)A 288 degree circular sector with radius 15 is rolled to form a cone. Find the height of the cone.

The perimeter of the base of the cone will be :

2 * pi * 15   (288/360)  =  

pi * 30/ 360 * 288

pi *  288/12  = 

24 pi

So....the radius of the cone is given by

24pi  = 2pi * r         divide both sides by 2 pi

12 =  r

The slant height will be the original radius of the sector  = 15

And this forms the hypotenuse  of  a   9 - 12 - 15     right triangle

And the radius forms one of the legs  = 12

So....the height forms the other leg  =  9

10)The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V cubic units and the total surface area of the frustum be A square units. Find V + A.

The height  =  4

The volume, V,  is given by

(1/3) * pi * height  ( [radius base 1]^2 +  product of the base radii +[ radius base 2]^2 )  =

pi / 3  *  4  * ( 12^2 +  12*9 + 9^2)

pi / 3 * 4 * ( 144 + 108 + 81 )

pi / 3 * 4  * ( 333)

pi * 4 * 111

444 pi

The surface area A, is given  by :

pi ( sum of radii) * √ [ (difference of radii)^2 + height^2 ] + pi (radius 1)^2 + pi (radius 2)^2

pi ( 21) √ [ 3^2 + 4^2 ] + pi  [ 144 + 81 ]

pi [  21 * 5 + 225 ]

pi [ 105 + 225 ] 

pi [ 330]

330 pi

So

V + A  =

[444 +330 ] pi  =

774 pi

3)A prism and a cone have the same base area and the same height. The volume of the prism is 1. What is the volume of the cone?

The base area of the cone  =  pi * r^2

But...this is also the base area of the prism

So.....the volume of the prism  =    base area * height  = 1

So

1  = base area * height

1  = pi (r^2) * height

1/ [ pi (r^2)]  =  height

So....the volume of the cone is

(1/3)[ pi * r^2]  [ 1 / [ pi * ^2 ]  =     1/3 

8)In the diagram, XY and XprimeYprime are diameters of the two bases of the cylinder, and XY is parallel to XprimeYprime. We know [XYYprimeXprime] = 30. Find the lateral surface area of the cylinder.

I'm assuming that  [ XYY'X']  represents the area of the cross-section....then  the area can also be represented by

2r * h

So

2r * h  = 30

r * h  = 15

So....the lateral surface area, based on this assumption is

2pi  *r * h    =

2pi (15)  = 

30 pi  units^2