3. A cub has the following measurements: I=0.045 m, w= 0.45dm, 4.5 mm. It's mass is 1.45 X 104 mg. What is this
cube's density in Kg/cm?

Density of cube = 1.59 × 10-⁴ kg/cm³

Explanation:

From the question, the dimensions of the cube are as follows:

Iength, l =0 .045 m, width, w = 0.45dm, height, h = 4.5 mm.

It's mass is 1.45 X 104 mg. What is this cube's density in Kg/cm?

First, all units of length are converted to cm and mass is converted to Kg.

L = 0.045 m = 0.045 m × 100 cm/m = 4.5 cm;

W = 0.45 dm = 0.45 dm × 10 cm/dm = 4.5 cm

Since it is a cube, the height, h = 4.5 cm not 4.5 mm

Mass of cube = 1.45 × 10⁴ mg = 1.45 × 10⁴ mg × 1 × 10-⁶ kg/mg = 0.0145 kg

Density = mass/volume

Volume of cube = s³ or l × w × h

Volume of cube = 4.5 cm × 4.5 cm × 4.5 cm = 91.125 cm³

Density of cube = 0.0145 kg / 91.125 cm³

Density of cube = 1.59 × 10-⁴ kg/cm³

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