Question

A manufacturer is making shipping boxes that are square prisms of base edge length a inches and height h inches. As per the requirement, the total surface area of the box must not exceed 1,500 square inches. What dimensions of the boxes can the manufacturer choose? Select all that apply.

Answer 1

A. a= 12, h =18

C. a= 10, h =20

Explanation:

Based on the information from the question, the formula to find the area of the prism will be:

area= 2 * (a*a) + 4 * (a*h)

area= 2a^2 + 4ah

Using the formula, we can do the calculation for each option to find if the area less than 1500 square inches as required. If we look closely, we can see that the edge length of the square (a) has highest exponent, thus have more influence on the area. So, we can guess that the high value of a will result in a high value of the surface area.

A. a= 12, h =18

area= 2a^2 + 4ah

area= 2(12)^2 + 4(12)(18)= 1152

true

B. a= 18, h =20

area= 2(16)^2 + 4(16)(20)= 1792

false

C. a= 10, h =20

area= 2(10)^2 + 4(10)(20)=1000

true

D. a= 20, h =10

area= 2(20)^2 + 4(20)(10)=1600

false

E. a= 25, h =10

area= 2(25)^2 + 4(25)(10)=2250

false