Question

A packaging company manufactures various sizes of boxes. Calculate the surface area of the box below. a.1200 mm b.430 mm c.510 mm Use the formula: SA = 2hl + 2hw + 2lw Give your answer in cm².

Answer 1

The surface area of the box with dimensions 1200 mm, 430 mm, and 510 mm is
`\( 2 * (12 * 43) + 2 * (12 * 51) + 2 * (43 * 51) \)`cm², resulting in a surface area of 57,150 cm².

Step-by-step explanation:

The formula for the surface area of a rectangular box is SA = 2hl + 2hw + 2lw, where h, l, and w represent the height, length, and width of the box, respectively. In this case, the given dimensions are 1200 mm, 430 mm, and 510 mm. To convert these measurements to centimeters, we divide each by 10 (since 1 cm = 10 mm).

The surface area calculation involves substituting these values into the formula:

`\[ SA = 2 * (12 * 43) + 2 * (12 * 51) + 2 * (43 * 51) \]`

Simplifying this expression yields the final result of 57,150 cm². The units are squared because surface area is a measure of two-dimensional space.

Understanding and applying the surface area formula is essential in various industries, especially in packaging where efficient use of materials is crucial. The calculated surface area helps determine the amount of material needed to manufacture the box and influences factors such as cost and packaging efficiency.