Question

You were interested in buying a gift that is shaped like a cube for your friend you have two different sizes to choose from one has a side length of 1.9ft and the other is 1.6ft in length you only have 36 square yd of wrapping paper. Is there enough wrapping paper for box 1, box 2 and both boxes

Answer 1

Answer:

Is there enough wrapping paper for both boxes

Step-by-step explanation:

we know that

The surface area of a cube is equal to

$SA=6b^{2}$

where

b is the side length of the cube

step 1

Find the surface area of box 1

we have

$b=1.9\ ft$

substitute in the formula

$SA=6(1.9)^{2}$

$SA=21.66\ ft^{2}$

step 2

Find the surface area of box 2

we have

$b=1.6\ ft$

substitute in the formula

$SA=6(1.6)^{2}$

$SA=15.36\ ft^{2}$

step 3

we have  36 square yd of wrapping paper

Convert square yards yo square feet

Remember that

1 yd=3 ft

$36\ yd^2=36(3^2)=324\ ft^2$

Adds surface area box 1 plus surface area box 2

$21.66+15.36=37.02\ ft^{2}$

$37.02\ ft^{2} < 324\ ft^2$

therefore

Is there enough wrapping paper for both boxes

Answer 2

Answer:

Step-by-step explanation:

Since a cube has 6 faces with equal lengths

Total surface area of Box 1= (1.9×1.9)6=21.66ft²

Total surface area of Box 2=(1.6×1.6)6=15.36ft²

Wrapping paper available=36yd²

Since 1yd²=9ft², convert 36yd² to ft²

36×9=324ft²

• For Box 1

324/21.66=14.96, meaning the wrapping paper is enough for 14 of the Box 1 type

• For Box 2

324/15.36=21, meaning the wrapping paper is enough for 21 of the Box 2 type

• For Both boxes

Total surface area of both boxes=21.66+15.36=37.02ft²

324/37.02=8.75,meaning the wrapping paper is enough for at least 8 of both Boxes