Volume and Surface Area Concepts

The video tutorial covers the calculation of volumes for cones, spheres, and cylinders. It begins with a word problem involving an ice cream cone and demonstrates how to calculate the volume of the cone using the formula for the volume of a cone. The tutorial then adds a spherical scoop to the cone and calculates the total volume. It also explores a new type of scoop in the shape of a cylinder and compares the volumes of different scoops. The tutorial concludes with a discussion on how scale factors affect volume.

What is the formula for the volume of a cone?

• V = πr²

• V = 4/3πr³

• V = 1/3πr²h

• V = πr²h

If a cone has a diameter of 1.5 inches, what is its radius?

• 0.75 inches

• 0.5 inches

• 1.5 inches

• 2 inches

What is the volume of a cone with a radius of 0.75 inches and a height of 4.5 inches?

• 5.1 cubic inches

• 3.5 cubic inches

• 4.2 cubic inches

• 2.6 cubic inches

What is the formula for the volume of a sphere?

• V = πr²h

• V = 4/3πr³

• V = 1/3πr²h

• V = πr²

If a sphere has a diameter of 2 inches, what is its radius?

• 2 inches

• 0.5 inches

• 1 inch

• 1.5 inches

What is the total volume of an ice cream cone with a sphere on top, if the cone is 2.6 cubic inches and the sphere is 4.2 cubic inches?

• 8.8 cubic inches

• 7.8 cubic inches

• 5.8 cubic inches

• 6.8 cubic inches

What is the formula for the volume of a cylinder?

• V = πr²h

• V = 1/3πr²h

• V = 4/3πr³

• V = πr²

If a cylinder has a diameter of 2 inches and a height of 2 inches, what is its volume?

• 6.28 cubic inches

• 4.2 cubic inches

• 3.14 cubic inches

• 8.4 cubic inches

How does the scale factor affect the volume of a shape?

• It affects the volume by the scale factor

• It affects the volume by the scale factor squared

• It does not affect the volume

• It affects the volume by the scale factor cubed

If the scale factor is 1/2, what is the new volume of a shape with an original volume of 4.2 cubic inches?

• 0.5 cubic inches

• 2.1 cubic inches

• 0.525 cubic inches

• 1.05 cubic inches