Question

The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? View Available Hint(s) The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? 2.75 gcm3×1 m×3 m×4 cm×1000 g1 kg 2.75 gcm3×1 m×3 m×(100 cm1 m)2×4 cm×1

Answer 1

The equation for the mass of the granite countertop is:

M=
`2.75(g)/(cm^3) * (1 kg)/(1000g)  *1m*3m*4cm* ((100 cm)^2)/(1 m^2)`

Explanation:

The density of an object is given by:

`\delta=(M)/(V)`

where:

δ: density (2.75 g/cm³)

M: mass of the object

V: volume of the object

Thus, the mass of the object is expressed as:

M=δ×V

Since the density of the granite is expressed in g/cm³, we have to convert the units of the expression to get the mass in kilograms.

`\delta=2.75 (g)/(cm^3) * (1kg)/(1000g)`

Since the width and length of the countertop is given in meter, we have to convert the units of the expression into cm.

V=
`1m*3m*4cm *((100 cm)^2)/(1 m^2)`

The mass of the counter top is expressed as:

M=
`2.75(g)/(cm^3) * (1 kg)/(1000g)  *1m*3m*4cm* ((100 cm)^2)/(1 m^2)`

Answer 2

equation: 2.75 g/cm^3 * 1 m *3 m* (100 cm/1 m)^2 *4 cm * (1 kg/1000 g)

Explanation:

countertop mass, m =?

density, ρ = 2.75 g/cm^3

wide, w = 1 m

long, l = 3 m

thick, t = 4 cm

countertop volume, V = w*l*t = 1 m *3 m*4 cm* (100 cm/1 m)^2

Isolating mass from density definition gives

ρ = m/V

m = ρ*V

m = 2.75 g/cm^3 * 1 m *3 m* (100 cm/1 m)^2 *4 cm * (1 kg/1000 g)