What is the length of the side (in cm) of a cube that has a density of 12.6 g/ml and a mass of 7.65 g?

• A. 0.50 cm
• B. 1.00 cm
• C. 2.00 cm
• D. 0.87 cm

Answer: (D)

Verified step by step guidance

1. Identify the given quantities: density (\( \rho \)) = 12.6 g/mL and mass (\( m \)) = 7.65 g. Remember that 1 mL is equivalent to 1 cm\(^3\) for volume units.
2. Use the density formula to find the volume (\( V \)) of the cube: \[ V = \frac{m}{\rho} \]. Substitute the given mass and density values into this formula.
3. Calculate the volume in cm\(^3\) (since 1 mL = 1 cm\(^3\)) using the formula from step 2, but do not compute the final number yet.
4. Recall that the volume of a cube is related to the length of its side (\( s \)) by the formula: \[ V = s^3 \].
5. Solve for the side length \( s \) by taking the cube root of the volume: \[ s = \sqrt[3]{V} \]. This will give the length of one side of the cube in cm.