The volume of a triangular prism is increased by a factor of 8. By what factor is the surface area of the figure increased?

QUESTION POSTED AT 02/12/2019 - 07:54 AM

Answered by answersmine AT 02/12/2019 - 07:54 AM

we  know that

larger\ volume=original\ volume*(scale\ factor)^{3}


larger\ surface\ area=original\ surface\ area*(scale\ factor)^{2}


Find the scale factor

we know that

(scale\ factor)^{3}=8 \\ scale\ factor=\sqrt[3]{8}=2

Find the factor of the surface area increased

(scale\ factor)^{2}=2^{2} =4


the answer is

the surface area increased by a factor of 4

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