2 Answers

InUser · Answer 1 · 2021-04-13T20:51:12+0000

Answer:

Scale factor =
(4)/(9)

Perimeter ratio = 4 : 9

Surface area ratio = 16 : 81

Volume ratio = 64 : 729

Explanation:

Volume ratio =
$\frac{\text{volume of small prism}}{\text{Volume of large prism}}$

=
(128)/(1458)

=
(64)/(729)

= 64 : 729

Scale factor =
$\sqrt[3]{\frac{\text{volume of small prism}}{\text{Volume of large prism}}}$

=
$\sqrt[3]{(64)/(729)}$

=
(4)/(9)

Perimeter ratio = Scale factor

=
(4)/(9)

= 4 : 9

Surface area ratio = (Scale factor)²

=
((4)/(9))^(2)

=
(16)/(81)

= 16 : 81

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