Explain what happens to the volume of a prism when its dimensions are tripled.
Answer: Is the volume going to be 9 times larger
27 times as large. you are just multiplying by 3, 3 times, and 3^3 is 27
yes.
yes, to a 's answer.
To understand what happens to the volume of a prism when its dimensions are tripled, let's break it down step by step:
1. Start with the definition of a prism: A prism is a 3-dimensional shape with two identical parallel bases and rectangular faces connecting the bases.
2. The volume of a prism is calculated by multiplying the area of its base by its height. So, V = base area × height.
3. When all dimensions of a prism are tripled, it means that each side length of the base and the height of the prism are multiplied by 3.
4. Let's assume the original base area is A and the original height is h.
5. After tripling the dimensions, the new base area becomes 3A (since each side length is tripled) and the new height becomes 3h.
6. Plugging these values into the volume formula, we get V = (3A) × (3h) = 9A × h.
7. As you can see, when the dimensions of the prism are tripled, the volume becomes 9 times larger than the original volume.
Therefore, the answer is indeed that the volume of a prism will be 9 times larger when its dimensions are tripled.