If I need to make a mold with a square base with a volume of exactly 28 cubic centimeters how many possible molds could I make?
The original question is to make molds for candles. 1x1X28 (height), 1x28X1 (height), 1x2x14(height), 1x14x2(height), 2x14x1(height), 1x4x7(height), 1x7x4(height), 7x4x1(height), 2x2x7(height), 2x7x2(height), totally 10 molds.
To determine the possible molds with a square base and a volume of 28 cubic centimeters, we need to consider the dimensions of the mold. Let's denote the side length of the square base as "x".
The formula for the volume of a rectangular prism is given by V = l * w * h. In the case of our mold, the length, width, and height are all equal to x since it has a square base. Therefore, the volume formula becomes V = x * x * x, which simplifies to V = x^3.
We know that the volume should be 28 cubic centimeters, so we can write the equation x^3 = 28. To find the value of x, we can solve this equation.
Taking the cube root of both sides, we get x = ∛(28). Calculating the cube root of 28 gives x ≈ 3.0366.
Since it's not possible to have a mold with fractional measurements, we need to consider the closest whole numbers that the side length x could be. In this case, x can be either 3 or 4 since those are the closest whole numbers to 3.0366.
Therefore, you have two possible molds: one with a side length of 3 centimeters and another with a side length of 4 centimeters.
infinite number even if no curvy tops
If it is rectangular then
x^2 h = 28
h = 28/x^2
if you want integer dimensions, then since
28 = 2^2 x 7
the mold must be 2x2x7 or 1x1x28