Question

7. Terrance needs to find the lateral surface area of the box shown below. Assuming that the base is the bottom of the prism, which of the expressions below will give him the correct lateral surface area?

Answer 1

To find the lateral surface area of a rectangular box, add the areas of the sides (lateral faces) using the formula Lateral Surface Area = 2h(l + w). For cylinders, use the formula Lateral Surface Area = 2πrh, with r being the radius of the circular base.

Step-by-step explanation:

To find the lateral surface area of a box, also known as a rectangular prism, you must add the areas of all the sides except for the base and top, which are the lateral faces. If the dimensions of the box are given as length (l), width (w), and height (h), the lateral surface area can be calculated using the formula: Lateral Surface Area = 2h(l + w).

Each pair of opposite sides are equal and contribute twice their area to the total lateral surface area, hence the term 2h in the formula. The height is the dimension that connects the base to the top, while l and w are the dimensions along the base.

For a prism with a circular base, such as a cylinder, the lateral surface area is calculated differently, using the circumference of the base circle (2πr) times the height of the cylinder: Lateral Surface Area of Cylinder = 2πrh.