Question

A glass candleholder in the shape of a triangular pyramid has a volume of 2,010 mm³. The base of the holder has a height of 13.4 mm and a base of 30 mm. What is the height of the candleholder?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height of the candleholder, we first need to calculate the height of the triangular pyramid.

The volume of a triangular pyramid is given by the formula: V = (1/3) x Base Area x Height

In this case, we are given that the volume is 2,010 mm³, the base has a height of 13.4 mm and a base of 30 mm.

First calculate the base area:
Base Area = (1/2) x base x height
Base Area = (1/2) x 30 mm x 13.4 mm
Base Area = 201 mm²

Now substitute the base area and volume into the volume formula to find the height:
2,010 mm³ = (1/3) x 201 mm² x Height
Height = 2,010 mm³ / ((1/3) x 201 mm²)
Height = 30 mm

Therefore, the height of the triangular pyramid candleholder is 30 mm.