Surface Area and Volume of 3D Figures

This video tutorial covers the calculation of surface area and volume for various three-dimensional figures, including prisms, cylinders, pyramids, cones, and spheres. It provides formulas and easy-to-remember methods for solving these problems, emphasizing the grouping of similar shapes to simplify memorization. The video also offers practical examples and visual aids to enhance understanding.

What is the general formula for calculating the volume of a prism or cylinder?

• Volume = (Base Perimeter x Height) / 2

• Volume = Base Area x Height

• Volume = Base Area + Height

• Volume = Base Area / Height

Tags

CCSS.7.G.B.6

How do you calculate the surface area of a prism?

• Surface Area = (Base Area + Height) / 2

• Surface Area = 2(Base Area) + (Base Perimeter x Height)

• Surface Area = Base Area + (Base Perimeter x Height)

• Surface Area = Base Area x Height

Tags

CCSS.7.G.B.6

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

• Volume = (Base Area x Height) / 3

• Volume = Base Area x Height

• Volume = Base Area + Height

• Volume = (Base Area x Height) / 2

Tags

CCSS.7.G.B.6

How is the surface area of a triangular prism calculated?

• Surface Area = 2(Base Area) + (Base Perimeter x Height)

• Surface Area = Base Area + (Base Perimeter x Height)

• Surface Area = (Base Area + Height) / 2

• Surface Area = Base Area x Height

Tags

CCSS.7.G.B.6

What distinguishes the volume formula of pyramids and cones from prisms and cylinders?

• It involves multiplying by 3

• It includes dividing by 3

• It uses the slant height instead of the base area

• It requires adding the base area twice

Tags

CCSS.HSG.GMD.A.3

How do you calculate the surface area of a cone?

• Surface Area = Base Area + (π x Radius x Slant Height)

• Surface Area = Base Area + (Base Perimeter x Height)

• Surface Area = (Base Area x Height) / 3

• Surface Area = Base Area + (Base Perimeter x Slant Height)

Which of the following is a correct statement about calculating the volume of 3D shapes?

• The volume of a cone is calculated the same way as a cylinder

• The volume of a pyramid is three times that of a prism with the same base and height

• The volume of a sphere is calculated using the base area

• The volume of a cylinder is 1/3 the base area times the height

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume formula for a sphere?

• Volume = (4/3)π x Radius^3

• Volume = π x Radius^3

• Volume = (4/3)π x Radius

• Volume = π x Radius^2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How is the surface area of a sphere calculated?

• Surface Area = 4π x Radius

• Surface Area = 2π x Radius^2

• Surface Area = 4π x Radius^2

• Surface Area = π x Radius^2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the relationship between the diameter and radius of a sphere when calculating its volume?

• The radius is half of the diameter

• The diameter and radius are interchangeable

• The diameter is half of the radius

• The diameter is twice the radius

Tags

CCSS.7.G.B.4