Tetrahedron's Volume Ratio

📌 CONCEPT: In this problem, we need to find the ratio of the volumes of two similar regular tetrahedrons with edge lengths 6 cm and 8 cm. The volume of a tetrahedron is given by the formula V = (1/3) * (edge length)^3. We will use the concept of similarity of figures to find the required ratio.

📐 RULE / FORMULA: According to the formula of the volume of a tetrahedron, if two tetrahedrons are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding edge lengths. This can be expressed as (V1/V2) = (a1/a2)^3, where V1 and V2 are the volumes of the smaller and larger tetrahedrons respectively, and a1 and a2 are their corresponding edge lengths.

💡 WORKED EXAMPLE: If the edge length of the smaller tetrahedron is 6 cm and that of the larger one is 8 cm, then the ratio of their volumes is given by (V1/V2) = (6/8)^3 = (3/4)^3 = 27/64.

⚠️ COMMON MISTAKE: Students often get confused in the formula and use the ratio of volumes as (V1/V2) = (a1/a2) instead of (a1/a2)^3, which leads to incorrect results.