Part 2: Calculations and Problem -Solving Students will complete a set of surface area calculation problems including: - Basic calculations for simple shapes (one for each shape) - Complex problems involving composite shapes (at least 3 compound shapes) - Word problems based on real-world scenarios (2 applications)

Sure, I can help you with that! Let's start with the basic calculations for simple shapes.

1. Simple Shapes:
a. Surface Area of a Cube:
The formula for the surface area of a cube is SA = 6s^2, where s is the length of one side of the cube.
For example, if the side length of the cube is 4 cm, the surface area would be SA = 6(4^2) = 96 cm^2.

b. Surface Area of a Sphere:
The formula for the surface area of a sphere is SA = 4πr^2, where r is the radius of the sphere.
For example, if the radius of the sphere is 5 cm, the surface area would be SA = 4π(5^2) = 100π cm^2.

c. Surface Area of a Cylinder:
The formula for the surface area of a cylinder is SA = 2πr(h + r), where r is the radius of the base and h is the height of the cylinder.
For example, if the radius of the base is 3 cm and the height is 10 cm, the surface area would be SA = 2π(3)(10 + 3) = 66π cm^2.

2. Composite Shapes:
Let's say we have a composite shape made up of a cube and a cylinder. The cube has a side length of cm, and the cylinder has a radius of 3 cm and a height of 10 cm.

To find the surface area of the composite shape, we need to find the surface area of each individual shape and then add them together.

The surface area of the cube is SA = 6(4^2) = 96 cm^2.

The surface area of the cylinder is SA = 2π(3)(10 + 3) = 66π cm^2.

The total surface area of the composite shape is 96 + 66π cm^2.

3. Word Problems:
Let's say we have a word problem where we need to find the surface area of a rectangular prism that is being used to store books.

The dimensions of the rectangular prism are length = 12 cm, width = 8 cm, and height = 6 cm.

To find the surface area, we need to calculate the area of each face and then add them together.

The area of the top and bottom faces is 12 x 8 = 96 cm^2.

The area of the front and back faces is 12 x 6 = 72 cm^2.

The area of the left and right faces is 8 x 6 = 48 cm^2.

The total surface area of the rectangular prism is 2(96) + 2(72) + 2(48) = 336 cm^2.

I hope this helps you with your surface area calculations! Let me know if you have any more questions.