Volume and Surface Area Formulas

This video tutorial covers various 3D shapes, including spheres, cylinders, cones, rectangular prisms, triangular prisms, square pyramids, and cubes. It explains how to calculate their volume and surface area, and discusses the number of faces, edges, and vertices for each shape. The video also introduces Euler's formula and demonstrates its application to these shapes.

What is the formula for the volume of a sphere?

• 4/3 πr³

• πr²h

• 1/3 πr²h

• 2πr²

How do you calculate the total surface area of a cylinder?

• 4/3 πr³

• 2πr² + 2πrh

• πr² + 2πrh

• πr²h

What is the slant height of a cone used for?

• Calculating the lateral surface area

• Determining the base area

• Calculating the volume

• Finding the radius

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Which formula represents the volume of a cone?

• 2πr²

• 1/3 πr²h

• 4/3 πr³

• πr²h

Tags

CCSS.7.G.B.6

How is the volume of a rectangular prism calculated?

• Length + Width + Height

• Length × Width × Height

• 2 × (Length + Width + Height)

• Length × Width

Tags

CCSS.7.G.B.6

What is the formula for the diagonal length of a rectangular prism?

• √(l² + w² + h²)

• 2(l + w + h)

• l × w × h

• l + w + h

Tags

CCSS.6.G.A.1

Which of the following is a method to calculate the area of a triangle?

• base + height

• base × height

• base × height × 2

• 1/2 × base × height

Tags

CCSS.7.G.B.6

What is the lateral area of a triangular prism based on?

• The perimeter of the base

• The base area

• The height of the prism

• The volume of the prism

Tags

CCSS.HSG.GMD.A.3

How is the volume of a square pyramid calculated?

• 1/3 × base area × height

• base area × height

• 1/2 × base area × height

• base area + height

Tags

CCSS.6.G.A.4

According to Euler's formula, what is the relationship between faces, vertices, and edges?

• Faces + Vertices - Edges = 1

• Faces + Vertices - Edges = 0

• Faces + Vertices - Edges = 3

• Faces + Vertices - Edges = 2

Tags

CCSS.6.G.A.4