Question

Dylan has two cubes of iron. The larger cube has twice the mass of the smaller cube. He measures the smaller cube. It's mass is 20 grams, and its density is 7.87 g/cm3. What's the larger cube's volume?

Answer 1

The volume of the larger iron cube, which has twice the mass of the smaller cube, is calculated using the formula for density. With the mass of the smaller cube being 20 grams and its density at 7.87 g/cm3, the larger cube's mass would be 40 grams. The volume of the larger cube is then approximately 5.08 cm3.

Step-by-step explanation:

The student's question relates to finding the volume of a larger cube of iron when the smaller cube's mass and density are known, and the larger cube has twice the mass of the smaller one. The mass of the smaller cube is given as 20 grams with a density of 7.87 g/cm3. We apply the formula for density where density (ρ) is equal to mass (m) divided by volume (V), rearranging it to solve for volume.

Step-by-Step Solution:

1. Calculate the mass of the larger cube by doubling the smaller cube's mass: 2 × 20 g = 40 g.
2. Use the density formula to find the volume of the larger cube: Volume (V) = mass (m) / density (ρ).
3. Insert the mass and density values into the formula: V = 40 g / 7.87 g/cm3.
4. Complete the calculation to get the volume: V ≈ 5.08 cm3.

Hence, the volume of the larger cube is approximately 5.08 cm3, assuming that the density remains constant between the two cubes.

Answer 2

density
`\rho`
is given by
`\rho = frac{m}{V}`
where m is the mass of the object
V is the Volume of the object

let m1 be the mass of the smaller cube
let m2 be the mass of the larger cube

you know that the larger cube has twice the mass of the smaller cube
or m2=2*m1

so apply this information into the density equation and you can determine the volume of the larger cube