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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? Enter your answer, as a decimal, in the box

User Jonua
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1 Answer

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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)

Step-by-step 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
(5)/(4)

Hence, the new volume is given by


Volume = 48((5)/(4) )^3


=48((125)/(64) )


=48(1.953125)


=93.75 \ {cm}^(3)

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

User Farid Rn
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