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

 

2. 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?

 

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

 

4. 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 (variable not roman numeral) cubic units and the total surface area of the frustum be A square units. Find V+A .

 Apr 12, 2019
 #1
avatar+104686 
+1

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

 

Vcylinder  =   pi ^r^2 * height

 

150 pi = pi ( 5/6 height)^2 * height

 

150  =  (25/36) * height^3

 

150 * 36  / 25    =  height^3

 

6 * 36    = height^3

 

216 =  height^3

 

6 = height

 

(5/6)(6) = radius  =  5

 

Surface area   =     pi * r^2  + 2pi * r * h  =   pi * 5^2  + 2pi (5)(6)  =  

 

25 pi  + 60 pi  =

 

85 pi units^2

 

 

cool cool cool

 Apr 12, 2019
 #2
avatar+104686 
+1

2. 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?

 

Cone volume =  (1/3) base area * height  =   1/3

 

cool cool cool

 Apr 12, 2019
 #3
avatar+104686 
+1

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

 

15 will be the slant height of the cone

 

To find the cone's circumference....we have that

 

(288/360)  * 2 pi * 15  =   24 pi

 

So...to find the radius of the cone, we have that

 

24 pi  =  2 pi * radius

 

24 =  2 * radius

 

12 = radius

 

Using the Pythagorean Theorem the height is 

 

sqrt ( 15^2 - 12^2 )  =  sqrt (225 - 144)  = sqrt (81)  =  9

 

 

cool cool cool

 Apr 12, 2019

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