Question

A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 48 cm³. If nickel plating costs $1 per cm² and silver plating costs $11 per cm², find the dimensions of the box to minimize the cost of the materials.

a) Length: 2.667 cm, Height: 2.667 cm
b) Length: 4.000 cm, Height: 4.000 cm
c) Length: 6.000 cm, Height: 2.000 cm
d) Length: 3.464 cm, Height: 3.464 cm

Answer 1

To minimize the cost of materials, the dimensions of the box that will have the smallest surface area are Length: 3.464 cm, Height: 3.464 cm.

Step-by-step explanation:

To minimize the cost of materials, we need to find the dimensions of the box that will have the smallest surface area. Let’s assume the side length of the square base is 'x' cm. The height of the box will also be 'x' cm.

The surface area of the box can be calculated using the formula: Surface Area = 4 * Area of the sides + Area of the bottom + Area of the top.

The volume of the box is given as 48 cm³, so we can write the equation: x * x * x = 48. When we solve for 'x', we find that x is approximately 3.464 cm.

Therefore, the dimensions of the box that minimize the cost of materials are: Length: 3.464 cm, Height: 3.464 cm.