The Maverick Movie Theater sells a small tub of popcorn for $1

Question

Customers have complained that the large tub is too wide to carry into the theater without spilling. The owner wants to change the base to be a 10-inch square instead. To keep the same volume, the owner thinks that the new tub will need to be 14 inches tall. She reasons that if the width gets two inches shorter, the height should grow by two inches.  

Answer 1

I googled your question and I was able to find the rest of the information needed to give you some help.

So, this question is about the large popcorn size, which is originally a cube with side lengths equal to 12 inches.

The owner wants to change the cube into a rectangular prism, which will NOT have all equal side lengths, and will have a base of 10 inches.

Our new large popcorn box will be made up of two base squares that are 10inches by 10 inches, and four rectangular sides that are 12 inches by 10 inches.

The question asks; "She reasons that if the width gets two inches shorter, the height should grow by two inches. Do you agree? If so, show how you know. If not, determine the new height of the tub."

The owner wants to keep the same volume with the new rectangular prism tub.

the volume for the original tub will be found using the formula for

volume of cubes; a³ = V

(12³) = V = 1728 in³

Now we know that the original volume of the large popcorn box is 1728 in³, we can find the volume of the new proposed design to see if we get the same value.

to find the volume of the owner's idea, we will use the formula for the volume of rectangular prisms;

V = length * width * height

l= 10, h= 10, h= 14

V = (10)(10)(14) = 1400 in³

The new height proposed by the owner, 14 inches, does not give us the same volume we had in the original large popcorn box.

To find the height we want, we can set up an equation where we solve for h.

1. we know we need to end up with a volume of 1728 in³
2. we also know that we will have a length of 10 and a width of 10, because of the new base

so, V = l * w * h

V= 1728 in³ ; l= 10 ; w= 10

1728 in³ = (10)(10)h

1728 in³ =100h

divide both sides by 100;

h = 17.28 inches

Answer 2

So the current dimensions are L=10 w=12 and h=12 as she believes the

width and height resepctfully decrease and increase by 2 inches.

current volume is 10*12*12 =1440

new volume shall be 10*10*14=1400

So she is close, but incorrect...

Instead,

Let H be the new height when the width

is decreased by 2. Then,

10*12*12 = 10*10*H

1440 = 100*H

H =1440/100

14.4 inches = 14 + 0.4 in <-- there are 16 tick marks per inch

on the ruler. 1/16 inch

=14 + 0.4*16 ticks/inch

= 14 + 6.4 ticks

The new height is between

14 and 6/16 inches = 14 and 3/8 inches

14 and 7/16 inches

Never saw popcorn boxes that large, sorry.