Exploring Volume of 3D Figures

This video tutorial covers the calculation of volume for various 3D figures, including rectangular prisms, right triangular prisms, pyramids, cylinders, cones, and spheres. Each section explains the formula used to find the volume, emphasizing the importance of understanding the base area and height for prisms and cylinders, and the unique formulas for pyramids, cones, and spheres. Practice problems are provided for each type of figure to reinforce learning.

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

• Volume = Length / (Width x Height)

• Volume = (Length x Width) / Height

• Volume = Length x Width x Height

• Volume = Length + Width + Height

Tags

CCSS.7.G.B.6

In the context of volume, why are units cubed?

• Because the calculations always involve three numbers

• Because volume measures a two-dimensional space

• Because volume is calculated using a cube

• Because volume measures a three-dimensional space

Tags

CCSS.5.MD.C.3A

CCSS.5.MD.C.3B

CCSS.5.MD.C.4

How do you determine the base of a right triangular prism for volume calculation?

• It's the longest side of the triangle.

• It's the triangular face of the prism.

• It's always one of the triangle's sides.

• It's the side it sits on.

What adjustment is made to the volume formula of a pyramid compared to a rectangular prism?

• Divide by 3

• Divide by 2

• Multiply by 3

• Multiply by 2

Tags

CCSS.HSG.GMD.A.3

Why is the volume of a pyramid divided by 3 in its formula?

• To simplify the calculation

• Because it's a third of the volume of a prism with the same base and height

• To account for its triangular base

• Because it has 3 sides

Tags

CCSS.HSG.GMD.A.3

What is the formula to calculate the volume of a cylinder?

• Volume = pi / (Radius^2 x Height)

• Volume = (pi x Radius)^2 / Height

• Volume = pi x Radius^2 x Height

• Volume = pi x Radius x Height

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How is the volume of a cone related to the volume of a cylinder?

• It's the same as the volume of the cylinder.

• It's one-third the volume of the cylinder.

• It's twice the volume of the cylinder.

• It's half the volume of the cylinder.

Tags

CCSS.3.MD.A.2

What does the 'height' in the volume formula of a cylinder refer to?

• The diameter of the base circle

• The radius of the base circle

• The distance from the base to the top

• The distance around the circle

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What role does pi play in the volume formulas for cylinders, cones, and spheres?

• It's used to calculate the height.

• It's used because these shapes have circular bases.

• It's used to simplify the formulas.

• It's used as a constant for all volume calculations.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a sphere?

• Volume = pi x Radius^2

• Volume = 3/4 pi x Radius^3

• Volume = 4/3 pi x Radius^3

• Volume = 2/3 pi x Radius^3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3