lateral surface area
Reading Passage 1
Lateral Surface Area in Action
When you wrap paper around a box, you need to know how much paper covers only the sides. This is called lateral surface area. It shows how much space covers the sides of a shape, not the top or bottom.
Look at a cube box with a square base. First, find the perimeter of the base. Each side is 6 cm, so the perimeter is 24 cm. The perimeter is the distance around the bottom, where the lateral faces wrap. Next, find the height. The box is 6 cm tall. Finally, use the formula S = P × h to find the lateral surface area. Multiply 24 cm by 6 cm to get 144 cm². This tells you how much paper covers the sides.
A company is making a cylindrical container for oatmeal. The base has a radius of 3 cm. The box is 15 cm tall. The formula S = 2πrh finds the lateral surface area of a cylinder. The company needs to know how much label paper wraps around the curved side.
Reading Passage 2
Lateral Surface Area in Action
When wrapping paper around a box, printing a label for a can, or covering only the sides of a building, knowing how much material is needed for just the side faces is important. This measurement is called lateral surface area, and it tells how much space covers only the sides of a shape, not the top or bottom.
Consider a cube-shaped box with a square base. First, the perimeter of the base is found by adding all four sides together. Each side measures 6 cm, so the perimeter equals 24 cm, which represents the distance around the bottom of the shape where the lateral faces wrap. Next, the height of the box is measured, which stands 6 cm tall. Finally, the formula S = P × h is used to find the lateral surface area, so 24 cm is multiplied by 6 cm to get 144 cm². This number shows exactly how much material is needed to cover the side faces, without including the top or bottom.
A company designing a cylindrical container for oatmeal faces a similar task. The container has a base with a radius of 3 cm and stands 15 cm tall. The formula S = 2πrh can be used to find the lateral surface area of a cylinder. Before printing a label that wraps around the curved face of the container, the design team must determine how much space the label will cover.
Reading Passage 3
Lateral Surface Area in Action
Whether wrapping paper around a box, printing a label for a can, or covering only the sides of a structure, accurately determining how much material is required for the side faces alone is essential. This measurement, known as lateral surface area, represents the total space covering only the sides of a shape, excluding the top and bottom.
Consider a cube-shaped box with a square base. The perimeter of the base is calculated first by summing all four sides; since each side measures 6 cm, the perimeter equals 24 cm, representing the distance encircling the bottom of the shape where the lateral faces wrap. The height of the box, measuring 6 cm, is then incorporated using the formula S = P × h, which determines the lateral surface area by multiplying the perimeter by the height. Multiplying 24 cm by 6 cm produces 144 cm², indicating precisely how much material is necessary to cover the side faces while excluding the top and bottom.
A company designing a cylindrical container for oatmeal encounters a comparable challenge. The container features a base with a radius of 3 cm and stands 15 cm tall. The formula S = 2πrh applies to determining the lateral surface area of a cylinder. Prior to printing a label that wraps around the curved face of the container, the design team must calculate how much space the label will cover.