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

Is there enough wrapping paper for both boxes

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

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