Question

PLEASE HELP Consider eight, eight-cubic centimeter (8 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio. Be sure to show all calculations leading to an answer.

Answer 1

$8=2*2*2\\8=2*2*2\\2*2*2*2*2*2=4*4*4\\s_{large}=4\\s_{small}=2\\\\SA_{large}=6s^2\\SA_{large}=6(4)^2\\SA_{large}=6(16)\\SA_{large}=96\\\\SA_{small}=8s^3\\SA_{small}=8(2)^3\\SA_{small}=8(8)\\SA_{small}=64\\\\96:64\\\frac{96}{32}:\frac{64}{32}\\3:2$

3 : 2