when the volume of a cube is given by V=S3, where S, is the lenght of a side. Find the lenght of a side of a cube if the volume is 500 cm3. And round the answer to three decimal places. can you solve this problem and show all steps with the solution?
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V = S^3 = 500
s = cube root of 500
Can you find the cube root?
Sure! To find the length of a side of a cube given its volume, we can use the formula V = S^3, where V represents the volume and S represents the length of a side.
In this case, we are given that the volume of the cube is 500 cm^3. We need to solve for S, the length of a side.
Step 1: Start with the formula V = S^3.
Step 2: Substitute the given volume, V = 500 cm^3.
500 = S^3
Step 3: To find the length of a side, we need to isolate S. To do this, we'll take the cube root of both sides of the equation.
∛500 = ∛S^3
Step 4: Simplify the cube root of 500.
∛500 ≈ 7.937
Step 5: Simplify the cube root of S^3.
∛S^3 = S
Step 6: Set the simplified cube root of 500 equal to S.
S ≈ 7.937 cm
Step 7: Round the answer to three decimal places.
S ≈ 7.937 cm (rounded to three decimal places)
Therefore, the length of a side of the cube is approximately 7.937 cm when the volume is 500 cm^3.