The volume of an ice cube is 16 000 mm3. The exact length of each edge of the ice cube can be written in simplest mixed radical form as 𝑝√𝑞3 where p and q are whole numbers. Determine the length of one edge of the cube.
∛16000 = 10∛16 = 20∛2
To find the length of one edge of the ice cube, we need to find the value of p and q.
We know that the volume of the cube is given by the formula:
Volume = (length of one edge)³
Given that the volume is 16,000 mm³, we can solve for the length of one edge as follows:
16000 = (p√q³)³
To simplify the expression, we can remove the cube from both sides:
∛16000 = p√q³
Taking the cube root of 16,000 gives:
∛16000 = ∛(80 ×200) = 40∛2
So, we have:
40∛2 = p√q
Since p and q are whole numbers, we can conclude that p = 40 and q = 2.
Therefore, the length of one edge of the ice cube is 40√2 mm.
To determine the length of one edge of the cube, we can use the formula for the volume of a cube:
Volume = side^3
Given that the volume of the ice cube is 16,000 mm^3, we can set up the equation:
16,000 = side^3
To find the side length, we need to solve for the cube root of 16,000.
Now let's break down the process step by step:
Step 1: Take the cube root of both sides of the equation:
∛16,000 = ∛(side^3)
Step 2: Simplify the right side of the equation:
∛16,000 = side
Step 3: Calculate the cube root of 16,000.
By using a calculator or a math software, we find that the cube root of 16,000 is 25.
Step 4: Substitute the value of the cube root into the equation to find the length of one edge of the cube:
side = 25
Therefore, the length of one edge of the cube is 25 mm.