Question

The volume of a triangular prism is increased by a factor of 8.

By what factor is the surface area of the figure increased?

Answer 1

we  know that

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

and

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

so

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

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

therefore

the answer is

the surface area increased by a factor of $4$

Answer 2

The need to cut the plastic by finding the measures of the angles (scale factor) is 4.

We have given,

Marcel is designing a circular necklace that will consist of 4 sections, each with a different color of plastic.

We  know that

What is the formula of larger volume?

larger volume=original volume×(scaler factor )^3

larger surface area =original surface area× (scaler factor)^2

To find the scale factor

we know that

(scalar factor)^3=8

Taking cube root on both sides

scale factor=2

Find the factor of the surface area increased

(scale factor)^2=2^2=4

Therefore, The surface area increased by a factor of 4.

To learn more about the surface area visit:

brainly.com/question/16519513#SPJ3