Volume and Area of Geometric Shapes

The video tutorial covers the volume of prisms and cylinders, focusing on Cavalieri's Principle and composite figures. It begins with a review of area calculations for basic shapes like triangles and circles. The tutorial then explains Cavalieri's Principle, which states that solids with the same height and cross-sectional area have the same volume. The video demonstrates how to calculate volumes of various shapes, including oblique cylinders and prisms, using specific formulas. It concludes with examples of composite figures, showing how to add or subtract volumes when dealing with complex shapes.

What is the formula to find the area of an equilateral triangle with side length 's'?

• 1/2 * s * sqrt(3)

• s^2

• 1/2 * s^2 * sqrt(3)

• s^2 * sqrt(3)

If a circle has a radius of 6.8, what is its area in terms of pi?

• 92.48 pi

• 13.6 pi

• 6.8 pi

• 46.24 pi

According to Cavalieri's Principle, when do two figures have the same volume?

• When they have the same base area and height

• When they have the same weight

• When they have the same shape

• When they have the same surface area

What is the formula for the volume of a cylinder?

• pi * r^2

• 2 * pi * r * h

• pi * r^2 * h

• pi * r * h

If the base area of a cylinder is 121 pi and the height is twice the radius, what is the height?

• 33

• 22

• 44

• 11

What happens to the volume of a rectangular prism if all its dimensions are doubled?

• It quadruples

• It doubles

• It increases eightfold

• It triples

How do you find the volume of a composite figure with a prism on top of another prism?

• Subtract the volume of the top prism from the bottom

• Divide the volume of the bottom prism by the top

• Add the volumes of both prisms

• Multiply the volumes of both prisms

When calculating the volume of a composite figure with a hole, what operation is used?

• Division

• Subtraction

• Addition

• Multiplication

In a composite figure with a cylinder inside another cylinder, what is the first step to find the volume?

• Multiply the volumes of both cylinders

• Subtract the volume of the smaller cylinder from the larger

• Divide the volume of the larger cylinder by the smaller

• Add the volumes of both cylinders

What is the volume of a cylinder with radius 18 and height 12?

• 972 pi

• 216 pi

• 3888 pi

• 2916 pi