Question

A rectangular object was found to have a mass of 1.278 kg and density of 4.98  g/cm3. Suppose that you knew that the length was 47 mm and the width was 61 mm. Using this information, compute the height of the rectangle in cm.

Answer 1

To find the height of the rectangular object, we can use the formula for volume and rearrange it to solve for the height. By plugging in the given dimensions and density, we can calculate the volume of the object. Then, using the formula for volume, we can solve for the height and find that it is 0.089 mm or 0.0089 cm.

Step-by-step explanation:

To calculate the height of the rectangular object, we first need to find its volume using the given length, width, and density. The formula for volume of a rectangular object is:

Volume = Length × Width × Height

Plugging in the given values:

Volume = (47 mm × 61 mm × Height)

Now, convert the density from g/cm³ to g/mm³:

Density = 4.98 g/cm³ = 4.98 g/(10 mm)³ = 4.98 g/1000 mm³

Since density = mass/volume, we can solve for volume:

Volume = mass/density = 1.278 kg/4.98 g/1000 mm³ = 1.278 kg/0.00498 kg/mm³ = 256.513 mm³

Now we can solve for Height:

(47 mm × 61 mm × Height) = 256.513 mm³ → Length × Width × Height = 256.513 mm³ → Height = 256.513 mm³/(47 mm × 61 mm)

Calculating the final result:

Height = 0.089 mm = 0.0089 cm

Answer 2

89.6 cm

Step-by-step explanation:

From the question,

Volume of the rectangular object = Mass/Density.

V = m/D.................. Equation 1

Given: m = 1.278 kg, D = 4.98 g/cm³ = 4980 kg/m³

Substitute into equation 1

V = 1.278/4980

V = 2.57×10⁻⁴ m³.

But,

V = lwh............... Equation 2

Where l = length of the rectangular object, w = width of the rectangular object, h = height of the rectangular object.

make h the subject of the equation

h = V/lw........... Equation 3

Given: V = 2.57×10⁻⁴ m³, l = 0.047 m, w = 0.061 m.

Substitute into equation 3

h = 2.57×10⁻⁴/(0.047×0.061)

h = 0.896 m

h = 89.6 cm