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**+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

CPhill
Oct 14, 2018

#2**+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 ???

CPhill
Oct 14, 2018