Question

The volume of this triangular prism is 247.5 cubic inches. What is the value of t?

t = __ inches

Answer 1

t = 9in

Explanation:

The formula of a volume of a prism:

`V=BH`

B - area of a base

H - height

In the base is the triangle.

The formula of an area of a triangle:

`A=(bh)/(2)`

b - base

h - height

We have V = 247.5 in³, b = 5 in, H = 11 in and h = t.

Therefore:

`B=(5t)/(2)`

Put them to the formula of a volume:

`247.5=\left((5t)/(2)\right)(11)`

`247.5=(55t)/(2)`

`247.5=27.5t` divide both sides by 27.5

`9=t\to t=9\ in`

Answer 2

Volume of a triangle is 1/2 base x height x length.

Using the given information we can find t:

247.5 = 1/2(5)(t)(11)

Simplify:

247.5 = 2.5(t)(11)

247.5 = 27.5t

Divide both sides by 27.5:

t = 247.5 / 27.5

t = 9