Calculating Volumes of Cylinders, Cones, and Spheres

This lesson covers the calculation of volumes for three types of 3D shapes: cylinders, cones, and spheres. It begins with an introduction to cylinders, explaining that they are a type of prism with congruent circular faces. The volume formula for a cylinder is derived and demonstrated with an example. The lesson then moves on to cones, explaining how their volume is a third of a cylinder's, and provides a step-by-step calculation. Finally, the lesson covers spheres, emphasizing the importance of correctly using the formula involving cubed radius, and provides an example calculation.

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

• V = 4/3πr^3

• V = πr^2h

• V = 2πrh

• V = 1/3πr^2h

How do you calculate the area of the circular base in a cylinder?

• r^2

• πr^2

• 2πr

• πr

What is the volume of a cylinder with a radius of 1.2 cm and a height of 3.5 cm?

• 15.83 cm^3

• 14.13 cm^3

• 16.23 cm^3

• 13.82 cm^3

How do you calculate the volume of a 3D shape?

• By multiplying the perimeter by height

• By multiplying the base area by height

• By dividing the area by the height

• By adding the area of all faces

How many cones fit into a cylinder of the same radius and height?

• 5

• 2

• 3

• 4

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

• V = πr^2h

• V = 1/3πr^2h

• V = 4/3πr^3

• V = 2πrh

What is the volume of a cone with a radius of 4 cm and a height of 8.2 cm?

• 128.67 cm^3

• 150.72 cm^3

• 145.26 cm^3

• 137.39 cm^3

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

• V = 1/3πr^2h

• V = 4/3πr^3

• V = πr^2h

• V = 2πrh

Why is it important to use the cube of the radius in the sphere volume formula?

• To calculate the surface area

• To simplify the calculation

• To account for the height

• To correctly calculate the volume

What is the volume of a sphere with a radius of 4 cm?

• 267.95 cm^3

• 256.68 cm^3

• 245.44 cm^3

• 278.23 cm^3