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 [tex]93.75 \ {cm}^{3}[/tex]
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, [tex]V=Bh[/tex]
Volume of the prism is given by
[tex]V=Bh[/tex]
[tex]V=(8)(6)[/tex]
[tex]V=46\ cm^3[/tex]
Thus, the volume of the prism is [tex]46 \ {cm}^{3}[/tex]
It is also given that the volume of the dilated prism is dilated by a factor of [tex]\frac{5}{4}[/tex]
Hence, the new volume is given by
[tex]Volume = 48(\frac{5}{4} )^3[/tex]
[tex]=48(\frac{125}{64} )[/tex]
[tex]=48(1.953125)[/tex]
[tex]=93.75 \ {cm}^{3}[/tex]
Thus, the volume of the dilated prism is [tex]93.75 \ {cm}^{3}[/tex]
