Question

A prism with a volume of 270 m³ is dilated by a factor of 3. What is the volume of the dilated prism?

Answer 1

1. 3^3 = 27, 27 x 270 = 7,290m^3

2. original volume = 8 x 6 = 48 cm^3

new volume = 48 x (5/4)^3 = 93.75 cm^3

 

Answer 2

Answer:

Step-by-step explanation:

When a geometrical figure is dilated by k units, we get area becomes k^2 times and volume k^3 times.

Given that a prism has original volume = 270m^3

Scale factor of dilation =3

Volume new would be = 3^3 (270)

=27(270)

=7290 m^3

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II) A prism has base area = 8 cm^2

Height = 6 cm

Dilated by scale factor = 5/4

New base area = 8(5/4)(5/4) = 25/2 cm^2

New height = 6(5/4) = 15/2

New volume = new base x new height

= 25/2*15/2 =375/4 = 93.75 cubic cm.