Question

Mr. Riojas is building his children a sandbox that is shaped like a triangular prism. He uses 7-foot-long wooden beams for each 'side of the base. He measures the height of the triangular base to be 6.1 feet. If he makes the sandbox 1 foot tall, how much sand will he need to fill it?

Answer 1

21.35
`ft^(3)`

Explanation:

It is given that the box is a triangular prism.

Side of Base of prism = 7 ft

Height of Base of prism = 6.1 ft

Area of a triangle is given as:

`B = (1)/(2) * \text {Base} * \text{Height}`

`\Rightarrow (1)/(2) * 7 * 6.1\\\Rightarrow 21.35\ ft^(2)`

Volume of a prism is:

`V = B * h`

B is the area of base of prism

h is the height of prism

Here, h = 1 foot

So, V = 21.35
`*` 1

Volume of prism is = 21.35
`ft^(3)`

Sand required to fill the triangular prism shape box is 21.35
`ft^(3)`.