Question

The volume of this triangular prism is 162 m³ what is the value of B?

Answer 1

Here, we are given a triangular prism.

Given:

Volume, V = 162 cubic meters

Height, h = 9 meters

Length, l = 6 meters

Base, b = ?

To find the base, b, of the triangular prism, use the formula for the volume of a triangular prism below:

`\begin{gathered} V=(1)/(2)\ast base\ast height\ast length \\ \\ V=(1)/(2)bhl \end{gathered}`

Rewrite the formula for b:

`\begin{gathered} V=(1)/(2)\text{bhl} \\ \\ \text{Multiply both sides by 2:} \\ 2V=\frac{\text{bhl}}{2}\ast2 \\ \\ 2V=\text{bhl} \\ \\ \text{Divide both sides by hl:} \\ (2V)/(hl)=\frac{\text{bhl}}{hl} \\ \\ (2V)/(hl)=b \\ \\ b=(2V)/(hl) \end{gathered}`

Now, input values into the equation:

`\begin{gathered} b=(2V)/(hl) \\ \\ b=(2\ast162)/(9\ast6) \\ \\ b=(324)/(54) \\ \\ b=6\text{ meters} \end{gathered}`

Therefore, the value of b is 6

ANSWER:

6 m