Question
What is the side length of a cube that has a volume of 343 cubic centimeters? Recall the formula Cube: \( v=s^{3} \)
Ask by Schneider Campbell. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The side length of the cube is 7 centimeters.
Solution
To find the side length of a cube with a volume of 343 cubic centimeters, we can use the formula for the volume of a cube, which is given by \( v = s^3 \), where \( v \) is the volume and \( s \) is the side length.
Given that the volume of the cube is 343 cubic centimeters, we can substitute this value into the formula and solve for the side length \( s \).
\[ 343 = s^3 \]
Now, we can solve for \( s \) by taking the cube root of both sides of the equation.
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[3]{343}\)
- step1: Write in exponential form:
\(\sqrt[3]{7^{3}}\)
- step2: Simplify the root:
\(7\)
The side length of the cube is 7 centimeters.
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Simplify this solution Bonus Knowledge
To find the side length of a cube with a volume of 343 cubic centimeters, we can rearrange the formula \( v = s^{3} \) to solve for \( s \). Taking the cube root of both sides gives us \( s = \sqrt[3]{343} \). Since \( 7 \times 7 \times 7 = 343 \), the side length \( s \) is 7 cm! Did you know that cubes have been used throughout history for various practical applications? Ancient Egyptians utilized cubic measurements in construction, while Greek mathematicians explored the properties of three-dimensional shapes in their studies of geometry. Cubes also appear in popular games like dice and Rubik’s cubes, making them both practical and fun!
