The surface area of prisms and cylinders is a fundamental concept in geometry, and mastering it is essential for students in grades 6, 7, 8, and high school. To help students ease into this concept, we have compiled a comprehensive ensemble of 50 worksheets on the surface area of prisms and cylinders. In this article, we will provide an overview of the worksheets, the formulas used to calculate the surface area, and some sample answers.

Surface Area of Prisms

The surface area of a prism is the sum of the areas of its bases and faces. The formula for the surface area of a prism is:

SA = 2B + L

where SA is the surface area, B is the area of the base, and L is the lateral area.

For example, find the surface area of a rectangular prism that is 12 inches long, 8 inches wide, and 4 inches high.

To find the surface area, draw a net of the rectangular prism. The surface area of the prism is the area of its net. The opposite faces of a rectangular prism are congruent.

Surface Area of Cylinders

The surface area of a cylinder is the sum of the areas of its curved surface and bases. The formula for the surface area of a cylinder is:

SA = 2πr(h + r)

where SA is the surface area, π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

For example, find the surface area of a cylinder with a radius of 4 inches and a height of 6 inches.

SA = 2π(4)(6 + 4) = 2π(4)(10) = 80π

Worksheets and Answers

Our comprehensive ensemble of 50 worksheets on the surface area of prisms and cylinders includes exercises on different solid figures, such as cubes, cones, cylinders, rectangular prisms, L-shaped prisms, and spheres. The worksheets are categorized based on a step-by-step approach involving counting unit squares to determine the SA, finding the surface area of nets, and then computing the surface area of geometrical shapes.

Some sample answers to the worksheets are:

• Find the surface area of a rectangular prism that is 12 inches long, 8 inches wide, and 4 inches high: SA = 2(12 x 8) + 2(12 x 4) + 2(8 x 4) = 192 + 96 + 64 = 352 square inches
• Find the surface area of a cylinder with a radius of 4 inches and a height of 6 inches: SA = 2π(4)(6 + 4) = 2π(4)(10) = 80π square inches

PDF Resources

To access the complete set of worksheets and answers, you can download our PDF resource package. The package includes:

• 50 worksheets on the surface area of prisms and cylinders
• Step-by-step solutions to each exercise
• Formulas and equations for calculating the surface area of different solid figures

By using our PDF resource package, students can practice and master the concept of surface area of prisms and cylinders, and teachers can use the worksheets as a supplement to their curriculum.