Answer: (6x-3y)3 or maybe not possible to do
Step-by-step explanation
multiply 3x2 and get 6. Multiply 3x3 and get 9.
Remark
All Cavaliere's principle says is that a slanted cylinder (for example) has the same volume as a cylinder with perpendicular parallel lines that the cylinder is sitting on.
I little known or maybe not a well emphasized fact is that the base is the same all the way up the cylinder. The coin picture below shows that. The basic formula for a Cavaliere cylinder is the same as for an ordinary cylinder.
See picture below
Formula
V = B * H
Sub and Solve
V = 1024
r = 8
p=3.14
V = pi*r^2 * h
1024 = 3.14*8^2 * h combine the right side.
1024 = 3.14*64 *h
1024 = 200.96 * h divide by 200.96
1024/200.96 = h
You are only getting 5 inches.
None of your answers work.The conversion to meters is going to give you an even smaller number. If you add a comment, I'll come back and edit this question.
1,250 is more then 1.25 because it’s a greater number
I have attached a screenshot with the images of the two popcorn bags used by the theater.
Part (a):Bag A:Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 inBag B:Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 inPart (b):To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3)
Surface area = 12 + 64 + 48
Surface area of bag A = 124 in²Bag B:Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4)
Surface area = 16 + 48 + 48
Surface area of bag B = 112 in²From the above calculations, we can deduce that
the theater should choose bag B in order to reduce the amount of paper needed.
Hope this helps :)