Question:
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
Answer:
The volume of the dilated prism is ![93.75 \ {cm}^{3}](https://tex.z-dn.net/?f=93.75%20%5C%20%7Bcm%7D%5E%7B3%7D)
Explanation:
A prism with a base area of 8 cm² and a height of 6 cm
The volume of the prism can be determined by the formula, ![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
Volume of the prism is given by
![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
![V=(8)(6)](https://tex.z-dn.net/?f=V%3D%288%29%286%29)
![V=46\ cm^3](https://tex.z-dn.net/?f=V%3D46%5C%20cm%5E3)
Thus, the volume of the prism is ![46 \ {cm}^{3}](https://tex.z-dn.net/?f=46%20%5C%20%7Bcm%7D%5E%7B3%7D)
It is also given that the volume of the dilated prism is dilated by a factor of ![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
Hence, the new volume is given by
![Volume = 48(\frac{5}{4} )^3](https://tex.z-dn.net/?f=Volume%20%3D%2048%28%5Cfrac%7B5%7D%7B4%7D%20%29%5E3)
![=48(\frac{125}{64} )](https://tex.z-dn.net/?f=%3D48%28%5Cfrac%7B125%7D%7B64%7D%20%29)
![=48(1.953125)](https://tex.z-dn.net/?f=%3D48%281.953125%29)
![=93.75 \ {cm}^{3}](https://tex.z-dn.net/?f=%3D93.75%20%5C%20%7Bcm%7D%5E%7B3%7D)
Thus, the volume of the dilated prism is ![93.75 \ {cm}^{3}](https://tex.z-dn.net/?f=93.75%20%5C%20%7Bcm%7D%5E%7B3%7D)