Volume Calculations of 3D Shapes

The video tutorial covers the calculation of volumes for spheres, hemispheres, and composite figures involving cones and hemispheres. It explains the formula for the volume of a sphere, 4/3 πr³, and demonstrates its application through examples. The tutorial also explores the volume of a hemisphere, which is half of a sphere's volume, and discusses composite figures combining cones and hemispheres. Finally, it compares the volumes of a sphere and a cylinder, highlighting the differences in their calculations.

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

• π r² h

• 2/3 π r³

• 4/3 π r³

• 4/3 π r²

How does the volume of a hemisphere compare to that of a full sphere?

• It is one-third the volume of a full sphere.

• It is half the volume of a full sphere.

• It is twice the volume of a full sphere.

• It is the same as a full sphere.

What additional information is needed to calculate the volume of a composite figure consisting of a cone and a hemisphere?

• The diameter of the cone

• The height of the cone

• The radius of the hemisphere

• The surface area of the hemisphere

How do you calculate the volume of a cube?

• Side length cubed

• 2/3 π r³

• 4/3 π r³

• π r² h

What is the difference in volume between a sphere and a cube when the side of the cube is 8 and the radius of the sphere is 4?

• 243.9 cubic inches

• 523.6 cubic inches

• 576.0 cubic inches

• 452.4 cubic inches

What is the formula for the volume of a cylinder?

• π r² h

• 1/3 π r² h

• 4/3 π r³

• 2/3 π r³

When comparing a sphere and a cylinder with the same radius, which has a greater volume if the height of the cylinder is 1.5 times the radius?

• The sphere

• They have the same volume

• It depends on the radius

• The cylinder

What is the coefficient of π r³ in the volume formula for a sphere?

• 2/3

• 1/3

• 4/3

• 1.5

What is the coefficient of π r³ in the volume formula for a cylinder with height 1.5 times the radius?

• 1/3

• 2/3

• 4/3

• 1.5

Which mathematical operation is used to compare the volumes of a sphere and a cylinder?

• Subtraction

• Division

• Multiplication

• Addition