Exploring Surface Area and Volume Concepts

This video tutorial covers the concepts of volume and surface area, focusing on right triangular prisms, square pyramids, triangular pyramids, and cubes. It provides step-by-step calculations for finding the volume and surface area of these shapes, using formulas and geometric principles. The tutorial also explains how to visualize these shapes using nets and highlights the differences between prisms and pyramids.

What formula is used to calculate the volume of a right triangular prism?

• Area of base + Lateral area

• Perimeter of base × Height

• Length × Width × Height

• Base area × Height

How do you find the surface area of a right triangular prism?

• Sum of the areas of all faces

• Base area × Height

• 2 × Base area + Lateral area

• Length × Width

How do you find the lateral area of a right triangular prism?

• Length × Width × Height

• Base area × Height

• Perimeter of base × Height

• 2 × (Base area) + Height

What is the area of the square base in a square pyramid with a side length of 8 inches?

• 128 square inches

• 16 square inches

• 32 square inches

• 64 square inches

If the square pyramid's floor is not painted, what is the surface area of the painted area?

• 184 square inches

• 160 square inches

• 64 square inches

• 224 square inches

How do you calculate the area of a triangle with a base of 8 and a height of 22?

• Base × Height

• Base + Height

• 1/2 × Base × Height

• 2 × (Base + Height)

What is the surface area of a triangular pyramid with sides of different lengths?

• Base area × Height

• Sum of the areas of all triangular faces

• Perimeter of base × Height

• Length × Width × Height

What is the first step in finding the surface area of a triangular pyramid?

• Multiply the base area by the height

• Calculate the area of each triangular face separately

• Calculate the area of the base

• Find the height using the Pythagorean theorem

What is the formula to find the surface area of a cube with a side length of 7 cm?

• (Side length)^2 + 6

• Side length^3

• Side length × 6

• 6 × (Side length)^2

What is the surface area of a cube with each side measuring 7 cm?

• 343 square cm

• 147 square cm

• 294 square cm

• 49 square cm