Thornton Surface Area

Fill in the Blank

Fill in the blank: The formula for the surface area of a prism is SA = 2B + ___, where B is the area of the base.

Open Ended

Explain how combining all the lateral faces of a prism as one big rectangle can help in finding the surface area more efficiently.

Multiple Choice

Surface Area = 2(length x width) + 2(length x height) + 2(width x height). For a rectangular prism with length 3.5 cm, width 4 cm, and height 4.5 cm, what is the total surface area?

• 95.5 cm²

• 45 cm²

• 72 cm²

• 56.5 cm²

Multiple Select

Which of the following are true about prisms?

• They have two congruent bases.

• They are named according to the shape of their bases.

• They have curved surfaces.

• They are bound on all sides by plane faces.

Multiple Choice

What is the formula for the total surface area (SA) of a right rectangular prism as shown in the slides?

• SA = 2B + Ph

• SA = 2πr^2 + 2πrh

• SA = lwh

• SA = 2lh + 2hw

Open Ended

What are prisms? Be ready to share.

Open Ended

Reflect on what you learned about the bases and lateral faces of different 3D solids. How do you think understanding these parts helps in finding the surface area of these shapes?

Multiple Choice

Which of the following solids has only one curved lateral face and one circular base?

• Cylinder

• Cone

• Sphere

• Rectangular Prism

Multiple Choice

Which of the following best describes the difference between lateral surface area and total surface area of a three-dimensional figure?

• Lateral surface area includes only the lateral faces, while total surface area includes both the bases and lateral faces.

• Lateral surface area includes only the bases, while total surface area includes only the lateral faces.

• Lateral surface area and total surface area are always equal.

• Lateral surface area includes the bases and total surface area includes only the lateral faces.

Fill in the Blank

The perimeter of the base of the triangular prism in the diagram is ___ cm.

Multiple Select

Which of the following steps are necessary to find the surface area of a triangular prism?

• Identify the bases and lateral faces

• Determine the perimeter of the base

• Calculate the area of the bases

• Ignore the lateral faces

Open Ended

Compare the process of finding the surface area of a prism to that of a cylinder. What are the similarities and differences in the formulas and steps?

Multiple Choice

Given a cylindrical paint roller with a diameter of 2.5 inches and a length of 10 inches, what is the lateral surface area in terms of π?

• 25π in²

• 10π in²

• 12.5π in²

• 5π in²

Multiple Choice

Which formula is used to calculate the surface area of a cylinder?

• SA = 2πr(r + h)

• SA = πr^2h

• SA = 2πrh

• SA = πr^2 + πrh

Multiple Select

Which of the following are necessary to calculate the surface area of a regular pyramid?

• Perimeter of the base

• Slant height

• Base area

• Volume

Open Ended

How do you approach finding the surface area of a pyramid when the base is not regular?

Fill in the Blank

The surface area of the irregular rectangular pyramid in slide 5 is ___ ft².

Multiple Choice

Which value is NOT needed to calculate the surface area of the cone in slide 6?

• 6.4 ft

• 5 ft

• 4 ft

• 10 ft

Fill in the Blank

To find the slant height s of a cone, you use the Pythagorean theorem: s = √(12² + ___²).

Multiple Choice

Which formula is used to determine the total surface area of a cone?

• SA = πrs + πr²

• SA = 4πr²

• SA = 2πrh + 2πr²

• SA = 2B + Ph

Multiple Choice

What is the formula for the surface area of a sphere?

• 4πr²

• πrs + πr²

• 2πrh + 2πr²

• 2B + Ph

Open Ended

Explain the difference between finding the surface area of a cone and a sphere. What formulas are used and what measurements are needed for each?

Multiple Select

Which of the following are necessary steps to determine the surface area of the composite figure made of a rectangular prism and a cylinder?

• Subtract the area of the overlapping circles

• Add the lateral surface area of the cylinder

• Add the total surface area of the prism without subtraction

• Add the area of the cylinder's base twice

Multiple Choice

What type of 3D solids comprise the composite figure in the last image?

• One square prism and one regular pyramid

• One rectangular prism and one cylinder

• One sphere and one cone

• One cube and one triangular prism