Question

The volume of a triangular prism is 90√3 cm3. If the radius of the inscribed circle in the base is 3 cm, find the altitude of the prism.

Answer 1

(drawing is not perfect)

I'm assuming this is a regular triangular prism so that the base is an equilateral triangle

Volume = area of base * height
altitude is another word for height

We have to use this formula to find the area of the base:
\(\bf area = 3r^2\sqrt{3}\)

What is the area of the triangle base given that the radius of the inscribed circle is 3 cm?


Once you know the area of the triangle base, you can find the altitude:

height = altitude = volume / area of base

The question tells you the volume is 90\(\sqrt{3}\). And you just calculated the area of the base using the formula I provided earlier. All you have to do now is divide the numbers to find the altitude.