Final answer:
To determine the height of the candleholder, calculate the area of the triangle at the base using the given measurements, then use the volume of the triangular pyramid to solve for the height using the volume formula.
Step-by-step explanation:
The question asks for the height of a glass candleholder in the shape of a triangular pyramid, given its volume and the measurements of its base. To find the height of the candleholder, we can use the formula for the volume of a triangular pyramid, which is V = (1/3) × base area × height. Here, the base area (A) can be calculated using the given base and height of the triangle at the base of the pyramid (b and h), using the formula A = (1/2) × b × h. Once we have the volume and the area of the base, we can rearrange the volume formula to solve for the height of the pyramid.
First, calculate the area of the base: A = (1/2) × b × h = (1/2) × 30 mm × 13.4 mm. Then, with the given volume, V = 2010 mm³, apply the volume formula of a pyramid and solve for the height (H): V = (1/3) × A × H. This gives us H = 3 × V / A.