Jamie just bought two boxes.

Question

Jamie just bought two boxes. The first box is square, with each side measuring 10 units, and is 4 units high. The second box is rectangular and has twice the volume of the square box. If the height of the second box is 5 units, and the width is 10 units, what is the length of the second box?

Answer 1

First let's identify the givens in this problem.

Box 1 is a square so it has equal measurements for the length and width, therefore . . .

Box 1 has length = 10, width = 10, and height = 4

Box 2 has length = unknown, width = 10, and height = 5

Volume for Box 2 is 2 times the Volume for Box 1, so V₂=2V₁

The formula for the volume of a rectangular prism (i.e. a box) is length times width times height (V = lwh),

so V₁ = l₁w₁h₁ or V₁ = (10)(10)(4) = 400 units

and V₂ = l₂w₂h₂ or V₂ = (x)(10)(5) = 50x units, with x representing the unknown length of Box 2

Substitute these values into the given statement V₂ = 2V₁ to get 50x = 2(400)

Solve for x

50x = 2(400)

50x = 800

x = 16

The height for Box₂ is 16 units.

Answer 2

Hello, so to approach this question the first thing you want to do is find the volume of the first box. We have the dimensions of the box being 10 by 10 by 4. To find the volume for this we multiply all the sides (10x10x4 = 400 units³). If the second box has twice the volume then we know the volume must be (2x400 = 800 units³). To find the missing side we create the following equation where 's' is the missing side 5*10*s = 800. Solving for s we get s = (800/50) = 16 units.

I am knew to this, so if this is not a detailed enough explanation or does not make sense please let me know and I will elaborate. Thanks!