Volume of Solids: Spheres and Cones

The video tutorial explains the relationship between the volumes of cones and cylinders, demonstrating how the volume of a cone is one-third that of a cylinder with the same base and height. It provides a step-by-step example of calculating the volume of a cone using given dimensions and solving a word problem to find the radius of a cone. The tutorial also introduces the formula for the volume of a sphere and provides an example calculation. Key concepts include understanding the geometric relationships and applying formulas to solve problems.

How is the volume of a cone related to the volume of a cylinder with the same base and height?

• The volume of a cone is one-third that of a cylinder.

• The volume of a cone is half that of a cylinder.

• The volume of a cone is twice that of a cylinder.

• The volume of a cone is equal to that of a cylinder.

What is the formula for the volume of a cone?

• V = 2/3 πr²h

• V = 4/3 πr²h

• V = 1/3 πr²h

• V = πr²h

In the example provided, what is the volume of the cone in terms of pi if the radius is 6 and the height is 9?

• 54π

• 144π

• 72π

• 108π

What is the approximate volume of the cone when calculated without using pi, given the radius is 6 and the height is 9?

• 360.5 cm³

• 314.2 cm³

• 400.1 cm³

• 339.3 cm³

In the word problem, what is the first step to find the radius of the cone-shaped funnel?

• Calculate the height of the funnel.

• Estimate the volume of the funnel.

• Draw a diagram of the funnel.

• Write down the volume formula for a cone.

What is the radius of the cone-shaped funnel if the volume is 314 cubic inches and the height is 12 inches?

• 7 inches

• 4 inches

• 5 inches

• 6 inches

What is the formula for the volume of a sphere?

• V = πr³

• V = 3/4 πr³

• V = 2/3 πr³

• V = 4/3 πr³

How do you calculate the volume of a hemisphere?

• Divide the volume of a sphere by 3

• Multiply the volume of a sphere by 3

• Divide the volume of a sphere by 2

• Multiply the volume of a sphere by 2

If the radius of a sphere is 4, what is its volume?

• 300 units³

• 268 units³

• 350 units³

• 320 units³

What is the volume of a hemisphere with a radius of 7 inches?

• 359.2 inches³

• 1436.8 inches³

• 1077.6 inches³

• 718.4 inches³