Volume of Cones and Pyramids

This video tutorial covers the calculation of volumes for pyramids, cones, and spheres. It begins with an introduction to the concept of volume in 3D shapes, focusing on pyramids and their base area and height. The tutorial then explains how cones are a special case of pyramids with a circular base, followed by the formula for the volume of spheres. It also includes calculations for hemispheres and frustums, and concludes with a problem involving the conversion of a sphere's volume into a cone's volume to determine the cone's height.

What is the volume of a pyramid if the base area is 30 square units and the height is 9 units?

• 120 cubic units

• 60 cubic units

• 270 cubic units

• 90 cubic units

If a pyramid has a square base with side length 10 cm and a height of 8 cm, what is its volume?

• 300 cm³

• 400 cm³

• 500 cm³

• 266.7 cm³

How is the volume of a cone related to the volume of a pyramid?

• A cone's volume is half that of a pyramid with the same base area and height.

• A cone's volume is twice that of a pyramid with the same base area and height.

• A cone's volume is the same as a pyramid with the same base area and height.

• A cone's volume is one-third that of a pyramid with the same base area and height.

What is the formula for the volume of a sphere with radius r?

• πr³

• 4/3 πr³

• 2/3 πr³

• 3/4 πr³

How do you calculate the volume of a hemisphere with radius 11 cm?

• 4/3 π(11)²

• 1/2 × 4/3 π(11)³

• 4/3 π(11)³

• 2/3 π(11)³

What is the volume of a cone with radius 3 cm and height 12 cm?

• 150 cm³

• 36π cm³

• 113.1 cm³

• 200 cm³

What is a frustum?

• A sphere cut in half

• A pyramid with a square base

• A cone with the top part removed

• A cone with a circular base

How do you find the volume of a frustum?

• Add the volumes of two cones

• Subtract the volume of the top cone from the whole cone

• Multiply the volume of a cone by two

• Divide the volume of a cone by two

If a solid sphere is melted to form a cone, what remains constant?

• The height

• The surface area

• The volume

• The radius

What is the relationship between the height and radius of a cone formed from a melted sphere?

• Height is twice the radius

• Height is half the radius

• Height is three times the radius

• Height is equal to the radius