Question

Drag & Drop: Place the correct solutions in each white box.

question one:
A box of Freebie Cereal is shaped like a rectangular prism and its dimensions are shown. The manufacture of Freebie Cereal wants to know the amount of cardboard needed to this box. Find the total surface area of the box in square inches.


question two:
Adele is buying wood to build a sandbox in her backyard. She does not need wood for the
bottom of the sandbox. The box is 4.5 feet long, 5.4 feet wide, and 2 feet high. Which of
the following is the closest to the lateral surface area of the sandbox?

Answer 1

1. question

To find the total surface area of the box, we need to find the areas of all six faces and then add them up. Let's call the length, width, and height of the rectangular prism l, w, and h, respectively. Then the surface areas of the six faces are:

Top and bottom faces: 2lw (there are two identical faces)

Front and back faces: 2lh (again, two identical faces)

Left and right faces: 2wh (and two identical faces here as well)

So the total surface area is:

2lw + 2lh + 2wh

Substituting the given dimensions of the Freebie Cereal box, we have:

2(10)(8) + 2(10)(12) + 2(8)(12)

= 160 + 240 + 192

= 592

Therefore, the total surface area of the Freebie Cereal box is 592 square inches.

2.question

The lateral surface area of a rectangular prism is the sum of the areas of all its faces except for the top and bottom faces. In this case, the sandbox has dimensions of 4.5 feet by 5.4 feet by 2 feet.

The area of the front and back faces is 2 x 2 x 5.4 = 21.6 square feet.

The area of the left and right faces is 2 x 2 x 4.5 = 18 square feet.

So the total lateral surface area is 21.6 + 18 = 39.6 square feet.

Therefore, the closest answer to the lateral surface area of the sandbox is 39.6.