Geometry Concepts and Formulas

The video tutorial covers various geometry topics, including calculating the volume of cones, cylinders, and spheres, determining the area of a sector, and understanding the properties of shapes like rhombuses and squares. It also explains how to find the radius of a circle using its equation and the distance formula, and how to calculate arc length. The tutorial includes practical examples and step-by-step calculations to help students understand these concepts.

If the height and radius of a cone are tripled, by what factor does the volume increase?

• 3

• 9

• 27

• 81

What is the formula for the volume of a cone?

• πr²h

• πr²h/2

• 1/3πr²h

• 2πr²h

How do you find the radius of a circle given a point on the circle and its center?

• Use the slope formula

• Use the midpoint formula

• Use the distance formula

• Use the area formula

What is the equation of a circle with center (1, 3) and radius 5?

• (x-1)² + (y-3)² = 5

• (x+1)² + (y+3)² = 5

• (x-1)² + (y-3)² = 25

• (x+1)² + (y+3)² = 25

How do you calculate the area of a sector of a circle?

• (arc measure/360) × πr²

• (arc measure/180) × 2πr

• (arc measure/180) × πr²

• (arc measure/360) × 2πr

If the arc measure is 80° and the radius is 13, what is the area of the sector?

• 130

• 150

• 160

• 118

What is the formula for the volume of a cylinder?

• πr²h/3

• πr²h/2

• 2πr²h

• πr²h

If a cylinder has a height of 9.5 cm and a diameter of 11 cm, what is its volume?

• 287

• 287π

• 2870

• 2870π

Which shape has opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors?

• Trapezoid

• Rectangle

• Rhombus

• Parallelogram

What is the equation of a circle with center (4, -7) and radius 4?

• (x-4)² + (y+7)² = 16

• (x+4)² + (y-7)² = 16

• (x-4)² + (y+7)² = 4

• (x+4)² + (y-7)² = 4