Exploring Unit Eleven Concepts

This video tutorial covers the concept of volume in geometry, focusing on prisms, pyramids, cylinders, and cones. It explains how to calculate the volume of these shapes using the area of the base and height, and introduces the concept of slant height in pyramids. The tutorial includes practical examples and calculations, emphasizing the importance of exact values in mathematical computations.

What is the formula for the volume of a prism?

• 1/3 area of the base times height

• Area of the base times slant height

• Area of the base times height

• 1/2 area of the base times height

How many pyramids with the same base and height are needed to fill a prism?

• Four

• Three

• Two

• Five

What shape are the lateral faces of a pyramid?

• Triangles

• Rectangles

• Squares

• Circles

What is the term for the height measured along the lateral face of a pyramid?

• Base height

• Lateral height

• Slant height

• Edge height

If the base area of a pyramid is 10 and the height is 16, what is the volume?

• 53.33

• 480

• 160

• 320

Which theorem is used to find the height of a pyramid when the slant height and half the base length are known?

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

• Euclidean algorithm

What is the formula for the volume of a cylinder?

• Area of the base times slant height

• 1/2 area of the base times height

• Area of the base times height

• 1/3 area of the base times height

What is the relationship between the volume of a cone and a cylinder with the same base and height?

• The cone's volume is half the cylinder's volume

• The cone's volume is one-third the cylinder's volume

• The cone's volume is the same as the cylinder's volume

• The cone's volume is twice the cylinder's volume

If the volume of a cylinder is 980π and it contains two congruent hollowed cones, what is the volume of the solid?

• 1960π

• 490π

• 980/3π

• 1960/3π

Caitlyn has three bags of sand, each containing 1200 cubic inches. If she needs 3750 cubic inches to build a sandcastle, will she have enough?

• Yes, she will have enough

• She will have more than enough

• No, she will not have enough

• She will have exactly enough