Question

Gary has a sheet of wrapping paper that is 96 cm long and 50 cm wide. He plans to use it to wrap a box with a surface area of 4,900 cm square. Does he have enough paper? If not, how much more paper does he need?

Answer 1

Answer: No it would not be enough , he will need 100 cm more of paper.

Step-by-step explanation:

First ,

The area of paper is

= 96 × 50

= 4800

How much more paper he needs = 4900 - 4800

= 100 cm

I hope this helps

Answer 2

To determine if Gary has enough paper to wrap the box, we need to calculate the surface area of the box and compare it to the area of the wrapping paper.

The surface area of the box can be found by adding up the area of all six sides. Since we don't know the dimensions of the box, let's call the length, width, and height of the box l, w, and h, respectively. Then the surface area of the box is:

SA = 2lw + 2lh + 2wh

We know that the surface area of the box is 4,900 cm^2, so we can set up the equation:

2lw + 2lh + 2wh = 4,900

Now we can rearrange this equation to solve for one of the variables. Let's solve for l:

l = (4,900 - 2lh - 2wh) / (2w)

Next, we can substitute the values given in the problem for the length and width of the wrapping paper, which are 96 cm and 50 cm, respectively. Then we can calculate the area of the wrapping paper:

Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2

Now we can compare the area of the wrapping paper to the surface area of the box. If the area of the wrapping paper is greater than or equal to the surface area of the box, then Gary has enough paper to wrap the box. Otherwise, he will need more paper. Let's plug in the values we have so far:

SA = 2lw + 2lh + 2wh
SA = 2(96)(50) + 2(96)(h) + 2(50)(h)
SA = 9,600 + 192h + 100h
SA = 9,600 + 292h

We know that SA = 4,900, so we can solve for h:

4,900 = 9,600 + 292h
-4,700 = 292h
h ≈ 16.1 cm

Now we can use this value to calculate the length and width of the box:

l = (4,900 - 2lh - 2wh) / (2w)
l = (4,900 - 2(96)(16.1) - 2(50)(16.1)) / (2(50))
l ≈ 45.8 cm

w = (4,900 - 2lh - 2wh) / (2l)
w = (4,900 - 2(96)(16.1) - 2(45.8)(16.1)) / (2(96))
w ≈ 27.8 cm

Now we can check if the area of the wrapping paper is greater than or equal to the surface area of the box:

Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2
Surface area of box = 2lw + 2lh + 2wh = 2(45.8)(27.8) + 2(45.8)(16.1) + 2(27.8)(16.1) ≈ 4,883.64 cm^2

Since the surface area of the box is less than the area of the wrapping paper, Gary has enough paper to wrap the box.