Question

An object in the shape of a rectangular prism has a length of 5 inches, a width of 3 inches, and a height of 2 inches. The object's density is 8.3 grams per cubic centimeter. Find the mass of the object to the nearest gram.

Answer 1

Answer:

$4,080grams$

Step-by-step explanation:

the formula for density is:

$d=\frac{m}{V}$

where d is density, m is mass, and V is volume.

solving for m in the last equation:

$m=d*V$

so if we find the volume and multiply it by the density $d=8.3gr/cm^3$  we will get the mass of the object.

The volume of a rectangular prism is given by:

$V=l*w*h$

where $l$ is length, $w$ is width and $h$ is height:

$l=5in\\w=3in\\h=2in$

we substitute to find the volume:

$V=5in*3in*2in\\V=30in^3$

since the density has units of $cm^3$ we need the volume also in units of $cm^3$ , so we make the conversion using:

$1in^3=16.3871cm^3$

multiplying by 30:

$30in^3=491.612cm^3$

and now we find the mass with the equation:

$m=d*V$

substituting d and V:

$m=(8.3gr/cm^3)(491.612cm^2)\\m=4,080.36gr$

the nearest gram is: $4,080grams$