Henry has a box that has 24 cm length, 27 cm width, and 10 cm height. He wants to cover the box with paper without any overlap.

A) How many square centimeters will be covered with paper?
B) Suppose the length and width of the box double. Does the surface area S double? Explain.
THANK YOU!!

henry wants to cover the box shown with paper without any overlap. how many square centimeters will be covered with paper?

386?

no

baljeet

A) To calculate the square centimeters covered by the paper, we need to find the surface area of the box. The box has 6 surfaces - a top, bottom, front, back, left, and right side.

The surface area of the top and bottom can be calculated by multiplying the length and width: 24 cm * 27 cm = 648 square cm each.

The surface area of the front and back can be calculated by multiplying the length and height: 24 cm * 10 cm = 240 square cm each.

The surface area of the left and right sides can be calculated by multiplying the width and height: 27 cm * 10 cm = 270 square cm each.

Now, we can sum up all the surface areas: 648 cm² + 648 cm² (top and bottom) + 240 cm² + 240 cm² (front and back) + 270 cm² + 270 cm² (left and right) = 2316 square cm.

Therefore, the paper will cover a total of 2316 square centimeters.

B) If the length and width of the box double, we need to determine if the surface area doubles as well.

The formula to calculate the surface area of a rectangular box is: S = 2lw + 2lh + 2wh.

Let's assume the original length and width are L and W, respectively. The original surface area is S = 2LW + 2LH + 2WH.

If the length and width double to 2L and 2W, the new surface area will be: S' = 2(2L)(2W) + 2(2L)(H) + 2(2W)(H) = 8LW + 4LH + 4WH.

Comparing the new surface area S' to the original surface area S, we can see that S' = 4S.

Therefore, when the length and width of the box double, the surface area will quadruple (multiply by 4), not double.

area = 2(24*27+24*10+27*10)

the area does not double:

original area: 2(xy+xz+yz)
new area: 2(2x*2y+2xz+2yz)