Okay, so I'm having trouble answering this math problem. Here we go: The base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm each. The volume of the prism...

Okay, so I'm having trouble answering this math problem. Here we go:

The base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm each. The volume of the prism is 0.075 cubic meters. Find the height of the prism.

Asked on by ghoulistic

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ishpiro | College Teacher | (Level 1) Educator

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The volume of any prism can be calculated using the formula

`V = h*B` , where h is the height of the prism and B is the area of the prism.

In this problem, the base is a right isosceles triangle. The area of such triangle will be `B = 1/2 a^2` , where a is the length of the equal sides. So in our case, the volume of the prism will be

`V = 1/2 ha^2`

Since the length of the equal sides is given in centimeters, but the volume of the prism is given in cubic meters, convert the value of a to meters before plugging it in:

a = 25 cm = 0.25 m.

Now we can plug in values of V and a into the formula above:

`0.075 m^3 = 1/2 h*(0.25)^2 m^2`

Multiplying both sides by 2 results in

0.15 m^3 = h*0.0625 m^2

From here, h can be found by dividing both sides by 0.0625:

`h=0.15/0.0625 m = 2.4 m`

The height of the given prism is 2.4 meters.

Sources:

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