Volume of Solids and Formulas

This video tutorial explains how to calculate the volumes of spheres, cones, and pyramids. It provides formulas and examples for each shape, demonstrating the calculations step-by-step. The video also includes an analogy to help understand the concept of volume displacement using a measuring jug. The tutorial emphasizes the relationship between the volumes of cones and cylinders, as well as pyramids and prisms.

What is the formula for calculating the volume of a sphere?

• 1/3 base area × height

• 1/3 π r² h

• π r² h

• 4/3 π r³

If a sphere has a radius of 7 cm, what is its volume in exact form?

• 217.82 cm³

• 1436.76 cm³

• 36,000 cm³

• 1370 2/3 π cm³

How much water will a sphere with a volume of 1436.76 cm³ displace in a measuring jug?

• 2000 cm³

• 1436.76 cm³

• 3600 cm³

• 563 cm³

What is the formula for calculating the volume of a cone?

• 1/3 base area × height

• π r² h

• 1/3 π r² h

• 4/3 π r³

Given a cone with a radius of 4 cm and height of 13 cm, what is its volume in exact form?

• 217.82 cm³

• 208/3 π cm³

• 1436.76 cm³

• 36,000 cm³

What is the volume of a cone with a radius of 4 cm and height of 13 cm, rounded to two decimal places?

• 36,000 cm³

• 208/3 π cm³

• 1436.76 cm³

• 217.82 cm³

What is the relationship between the volume of a cone and a cylinder with the same base and height?

• The cone's volume is half the cylinder's volume

• The cone's volume is twice the cylinder's volume

• The cone's volume is equal to the cylinder's volume

• The cone's volume is one-third of the cylinder's volume

What is the formula for calculating the volume of a pyramid?

• 1/3 base area × height

• π r² h

• 4/3 π r³

• 1/3 π r² h

If a square-based pyramid has a base area of 3600 cm² and a height of 30 cm, what is its volume?

• 217.82 cm³

• 208/3 π cm³

• 36,000 cm³

• 1436.76 cm³

How does the volume of a pyramid compare to a prism with the same base and height?

• It is half the prism's volume

• It is equal to the prism's volume

• It is one-third of the prism's volume

• It is twice the prism's volume