Sarah has two similar rectangular boxes. The dimensions of Box 1 are four times those of Box 2. How many times greater is the surface area of Box 1 than the surface area of Box 2?

8

64

4

16

16

Step-by-step explanation:

an area is always calculated by multiplying 2 dimensions.

when changing the dimensions, then the change factors for EACH dimension go into the calculation too.

therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.

this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.

just think

16×a + 16×b + 16×c ... = 16×(a+b+c+...)

and you understand why.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse