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Question 1: What is the total surface area, in square inches, of a cube with a volume of 1 cubic foot?

 

Question 2: 

 

Question 3: A round pizza is 1/3 of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece? Express your answer in terms of pi.

shreyas1  Oct 14, 2018
 #1
avatar+90968 
+1

Question 1: What is the total surface area, in square inches, of a cube with a volume of 1 cubic foot?

 

 L = W  = H...and all of these must  = 1   since  1 * 1 *  1  =  1 ft^3

So...each side is a 1 x 1 square

So...the total surface area  is

6 * [ 1 x 1  ]  =   6 ft^2

 

 

Question 3: A round pizza is 1/3 of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece? Express your answer in terms of pi.

 

Volume  =  (1/3)  * pi * (diameter / 2)^2  =  (pi / 3 ) * [ 6 ] ^2 =  12 pi in^3

 

If it is cut into  12 congruent pieces...each piece must have a volume of pi in^3

 

 

cool cool cool

CPhill  Oct 14, 2018
 #2
avatar+90968 
+1

Question 2

 

I am NOT  sure about this one...but I'll venture an answer

 

I believe that we have the frusum of a triangular prism.....

 

Assuming that CP /CQ    = DN /MD   ...we have that

 

CP =  CQ * DN / MD  =  8  * 2/4 =  16/ 4  = 4

 

The area of MDN  =  A   =  (1/2) (DN)(MD)sqrt3 / 2  =  (8/4) * sqrt 3 = 2sqrt 3

The area  of QCP  = B  =   (1/2) (CP)(CQ)sqrt3 /2  = (32/4)sqrt3 = 8sqrt3

 

The fomula for the volume  a prismatic frustum is similar  [ I think ] to that of a conical frustum

 

The volume is given by :

 

(1/3) ( height)  [ A + B  +  sqrt (AB)  ] = 

 

(1/3) (12) ( 10sqrt 3  + sqrt [ 16 * 3] )  =

 

4 ( 10 sqrt 3  +  sqrt 48  )  =

 

4 [ 10srt 3 + 4sqr3  ]  =

 

4 [ 14 sqrt 3 ]  =

 

56sqrt 3    units^3 

 

Can  anyone double-check this  ???

 

cool cool cool

CPhill  Oct 14, 2018
 #3
avatar+462 
+1

Question 1 asks for the answer in square inches so it has to be 864 inches squared. 

shreyas1  Oct 14, 2018
 #4
avatar+90968 
+1

Oops...sorry I missed that, shreyas1......!!!

 

You are corect  6 (12 x 12)  =  6 (144)  =  864 in^2

 

cool cool cool

CPhill  Oct 14, 2018

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