Question

What effect would tripling all the dimensions of a triangular prism have on the volume of the prism? Complete the explanation.

If both the base and height of the triangular base are tripled, the area of the base is multiplied by _______ . Tripling the height of the prism as well means the volume of the prism is multiplied by _______.

Answer 1

Upon tripling all dimensions of a triangular prism, the area of the base is multiplied by 9 since area calculation involves squaring the linear dimensions. When the prism's height is also tripled, the overall volume is multiplied by 27, as volume calculation is cubic in nature.

Step-by-step explanation:

When tripling all the dimensions of a triangular prism, the change in volume is significantly more than just tripling. The formula for the area of a triangle is 1/2 × base × height. So, if both the base and height of the triangular base are tripled, the area is not just tripled; it's multiplied by 3 for the base and 3 for the height. This results in the area being multiplied by 3², which is 9.

Now, considering the volume of the prism is the base area times the height of the prism (V = Ah), if the height is also tripled in addition to the base area being multiplied by 9, the change in volume is 9 (from the base area) times 3 (from the height), resulting in the volume being multiplied by 27.

Therefore, if both the base and height of the triangular base are tripled, the area of the base is multiplied by 9. Tripling the height of the prism as well means the volume of the prism is multiplied by 27.

Answer 2

If you triple the length of a single dimension object, you get x3 the size. If you triple the area of a 2nd dimension object, you get x3^2 the size. If you triple the volume of a three-dimensional object you get x3^3 the size.

The base will be x3^2 or 9 times larger.

If you triple the height as well as the base, you are increasing 3 dimensions, so you are increasing the volume to the third power, or 27 times larger.

9, 27