Exploring Surface Area Concepts

This video tutorial covers the calculation of surface areas for various 3D shapes, including cubes, triangular prisms, triangular pyramids, square pyramids, and rectangular prisms. It provides step-by-step instructions and examples, such as using shrink wrap for cubes and solving word problems involving pyramids and cubes. The tutorial also includes a practical application of calculating the cost of covering a shoe box based on its surface area.

What is the surface area of a cube with each side measuring 3 inches?

• 216 square inches

• 108 square inches

• 54 square inches

• 27 square inches

How many square inches of shrink wrap are needed to wrap five game cubes with a surface area of 54 square inches each?

• 540 square inches

• 324 square inches

• 108 square inches

• 270 square inches

How do you calculate the total surface area of a triangular prism?

• Multiply the base area by the height

• Double the area of the triangle and add the area of the rectangles

• Add the area of the base to the lateral surface area

• Sum the areas of all faces

What formula is used to find the area of a triangle?

• Base plus height

• Length times width

• Base times height

• Base times height divided by two

What is the lateral surface area of an equilateral triangular pyramid with a base of 12 and height of 8?

• 96 square feet

• 144 square feet

• 288 square feet

• 192 square feet

If a square pyramid and a cube have the same surface area, and the cube's width is 6 feet, what is the slant height of the square pyramid?

• 5.8 feet

• 12 feet

• 10 feet

• 6 feet

How do you find the missing height of a triangle in a pyramid with a total surface area of 336 square inches?

• Divide the total area by the base area

• Subtract the base area from the total and solve for height

• Multiply the base area by the height

• Use the Pythagorean theorem

Between two rectangular prisms, A and B, which has a greater total surface area if A's dimensions are 12 by 6 and B's are 15 by 6?

• Cannot be determined

• Prism B

• Both have the same

• Prism A

What is one side of a cube if its total surface area is 390 square centimeters?

• Less than 8 centimeters

• More than 10 centimeters

• Exactly 8 centimeters

• Between 8 and 9 centimeters

What is the cost to cover three pairs of shoes if one shoe box has a surface area of 400 square inches and the paper costs 2 cents per square inch?

• $8

• $12

• $6

• $24