After a 2 in. slice iscut off the top of a cube, the resulting solid has a volume of 32 in.2Find the dimensions of the original cube.
First of all, volume is in cubic units (e.g., 32 in^3).
Volume must be the product of the three dimensions. If one dimension is 2", the other two dimensions must multiply to make 16. Thus, the other two dimensions must be 4". Since it is a cube, all sides must have originally been 4".
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After a 2 inch slice is cut off the top of a cube the resulting solid has a volume of 32 cubic inches find the dimension of the original cube
To find the dimensions of the original cube, we can follow a step-by-step process.
Step 1: Understand the problem
The problem states that a 2-inch slice is cut off the top of a cube, and the remaining solid has a volume of 32 in^2. We need to find the dimensions of the original cube.
Step 2: Identify the known and unknown variables
We know that the resulting solid's volume is 32 in^2. The unknown variables are the dimensions of the original cube.
Step 3: Define the problem mathematically
Let's assume the side length of the original cube is 'x' inches. After cutting off the 2-inch slice, the remaining solid's volume can be represented as:
Volume_of_remaining_solid = (x - 2)^3 = 32 in^3
Step 4: Solve the equation
Taking the cube root of both sides to undo the cubing operation:
x - 2 = ∛(32) = 3
Solving for 'x', we add '2' to both sides:
x = 3 + 2 = 5
So, the side length of the original cube is 5 inches.
Step 5: Verify the answer
To verify, we can calculate the volume of the original cube:
Volume_of_original_cube = x^3 = 5^3 = 125 in^3
We can now check if the resulting volume is indeed 32 in^2:
Volume_of_remaining_solid = (x - 2)^3 = (5 - 2)^3 = 3^3 = 27 in^3
The resulting volume is not 32 in^2 but 27 in^3. Therefore, there may be an error in the problem statement or calculations.
It is crucial to double-check the problem statement and calculations to ensure the accuracy of the answer.