Question

Cathy wants to pack 100 gifts. The packaging includes a closed box made out of cardboard. The dimensions of the box are 11 cm long, 8 cm wide, and 8 cm high. In square centimeters, what is the minimum amount of cardboard Cathy needs to package all the gifts?

A. 38400 cm²
B. 39200 cm²
C. 48000 cm²
D. 50000 cm²

Answer 1

To find the minimum amount of cardboard Cathy needs, calculate the total surface area of the box and multiply it by the number of gifts. In this case, the correct answer is 48000 cm².

Step-by-step explanation:

To calculate the minimum amount of cardboard Cathy needs, we need to find the surface area of the box and then multiply it by the number of gifts. The surface area of a closed box can be calculated by finding the sum of the areas of its six faces.

In this case, the box has three pairs of faces with equal dimensions.

1. Two faces have dimensions 11 cm x 8 cm, so their total area is (11 cm x 8 cm) x 2 = 176 cm².
2. Two faces have dimensions 8 cm x 8 cm, so their total area is (8 cm x 8 cm) x 2 = 128 cm².
3. The remaining two faces have dimensions 11 cm x 8 cm, so their total area is (11 cm x 8 cm) x 2 = 176 cm².

Adding up these areas, we get 176 cm² + 128 cm² + 176 cm² = 480 cm². Since Cathy has 100 gifts, she will need 100 boxes, so the total amount of cardboard needed is 480 cm² x 100 = 48,000 cm². Therefore, the correct answer is option C. 48000 cm².