Question

2) If a brick has a length of 13.77 cm, a width of 8.50 cm, and a height of 5.12 cm:

a) What is the volume of the brick?
b) If the brick has a mass of 895.3 g, what is its density?

Answer 1

The volume of the brick is 600.1664 cm³, and with a mass of 895.3 g, the density is calculated to be 1.491 g/cm³.

Step-by-step explanation:

The volume of a brick with dimensions length 13.77 cm, width 8.50 cm, and height 5.12 cm is calculated by multiplying these three measurements. The formula for volume V is V = length × width × height.

The calculated volume is:

V = 13.77 cm × 8.50 cm × 5.12 cm

V = 600.1664 cm³

To find the density (ρ), which is mass per unit volume, the formula is ρ = mass / volume. Using the given mass of 895.3 g, we find the density as follows:

ρ = mass/volume

ρ = 895.3 g / 600.1664 cm³

ρ = 1.491 g/cm³

This method involves dimensional analysis and applying principles of mass and volume.

Answer 2

a. 599 cm³

b. 1.49 g/cm³

Step-by-step explanation:

A. Volume

Volume is the amount of space an object occupies. Since this is a brick, the object is a rectangular prism. The formula for the volume of a rectangular prism is the product of length, width, and height.

`V= l *w*h`

The brick's length (l) is 13.77 centimeters, the width (w) is 8.50 centimeters, and the height (h) is 5.12 centimeters. Substitute these values into the formula.

`V= 13.77 \ cm * 8.50 \ cm * 5.12 \ cm`

Multiply the numbers together.

`V= 117.045 \ cm^ 2* 5.12 \ cm`

`V= 599.2704 \ cm^3`

The original measurements have at least 3 significant figures, so our answer must have 3. For the number we calculated, that is the ones place. The 2 in the tenths place tells us to leave the 9 in the ones place.

`V \approx 599 \ cm^3`

`\bold {The \ volume \ of \ the \ brick \ is \ approximately \ 599 \ cubic \ centimeters}}`

2. Density

Density is the amount of matter in a specified space. The formula for density is mass over volume.

`d= (m)/(v)`

The mass of the brick is 895.3 grams and we just found the volume to be 599.2704 cubic centimeters. Substitute the values into the formula.

`d= (895.3 \ g)/(599 \ cm^3)`

Divide.

`d= 1.494657763 \ g/cm^3`

Round to three significant figures. For the number we calculated, that is the hundredth place. The 4 in the thousandth place tells us to leave the 9 in the hundredth place.

`d \approx 1.49 \ g/cm^3`

`\bold {The \ density\ of \ the \ brick \ is \ approximately \ 1.49 \ grams /cubic \ centimeters}}`