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baherus [9]
3 years ago
7

A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 . What is the volume of the dilated prism? E

nter your answer, as a decimal, in the box
Mathematics
1 answer:
Aliun [14]3 years ago
3 0

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}

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

Volume of the prism is given by

V=Bh

V=(8)(6)

V=46\ cm^3

Thus, the volume of the prism is 46 \ {cm}^{3}

It is also given that the volume of the dilated prism is dilated by a factor of \frac{5}{4}

Hence, the new volume is given by

Volume = 48(\frac{5}{4} )^3

             =48(\frac{125}{64} )

             =48(1.953125)

             =93.75 \ {cm}^{3}

Thus, the volume of the dilated prism is 93.75 \ {cm}^{3}

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