Solving for Volume Ratio?

📌 CONCEPT: The volume of a three-dimensional object, such as a prism, is directly proportional to the cube of its linear dimensions. When the dimensions of an object are altered, its volume changes accordingly. In this case, we need to find how a factor of 3 in one direction affects the volume of the triangular prism.

📐 RULE / FORMULA: The formula to calculate the volume of a prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height. When the dimensions are altered, the new volume is calculated by V' = (l'w'h'), where l', w', and h' are the new dimensions.

💡 WORKED EXAMPLE: Suppose we have a triangular prism with a trapezoidal base, where the parallel sides are 8 cm and 12 cm, and the height is 6 cm. If the prism is stretched by a factor of 3 in one direction, the new dimensions will be 8*3 = 24 cm, 12*3 = 36 cm, and 6*3 = 18 cm. The new volume will be V' = 24 * 36 * 18.

⚠️ COMMON MISTAKE: Students often forget to account for the change in dimensions when calculating the new volume. They might simply multiply the original volume by 3, instead of considering the new dimensions. It is essential to calculate the new volume using the correct dimensions.