Question

A right angled triangular prism has length 3m, breadth 2m and height 2.5m. If the mass of the prism is 3.4kg, find its density​

Answer 1

The density of the prism is 0.453 kilograms per cubic meter.

Explanation:

Let suppose that mass in the prism is uniformly distributed. Then, the definition of density (
`\rho`), in kilograms per cubic meter, is defined by the equation below:

`\rho = (m)/(V)` (1)

Where:

`m` - Mass, in kilograms.

`V` - Volume of the right angle triangle prism, in cubic meters.

Besides, the volume of the right angle triangle prism is:

`V = (1)/(2)\cdot b\cdot h\cdot l` (2)

Where:

`b` - Breadth of the base, in meters.

`h` - Height of the base, in meters.

`l` - Length of the base, in meters.

If we know that
`b = 2\,m`,
`h = 2.5\,m`,
`l = 3\,m` and
`m = 3.4\,kg`, then the density of the prism is:

`V = 7.5\,m^(3)`

`\rho = 0.453\,(kg)/(m^(3))`

The density of the prism is 0.453 kilograms per cubic meter.