Area and Circumference Concepts

This video tutorial focuses on solving problems related to the area and circumference of circles and squares. It introduces the formulas for circumference and area, explains how to calculate these for given dimensions, and explores dividing areas into halves and quarters. The tutorial also covers the concept of ratios between new and original areas, and provides algebraic expressions for semi-circles and quarter circles.

What is the primary focus of Lesson 18 in Module 3?

• Solving for the volume of a cube

• Solving for the surface area of spheres

• Solving for the area and circumference of circles and squares

• Solving for the perimeter of triangles

Which formula represents the circumference of a circle using the diameter?

• 2πr

• πd

• πr²

• d/2

How do you calculate the area of a square?

• Length × Width

• d/2

• πr²

• 2πr

If a circle has a diameter of 12 cm, what is its radius?

• 6 cm

• 24 cm

• 12 cm

• 3 cm

What is the area of a square with a side length of 12 cm?

• 72 cm²

• 36 cm²

• 24 cm²

• 144 cm²

How can you find half the area of a shape?

• Subtract 2

• Multiply by 2

• Divide by 2 or multiply by 0.5

• Add 2

What is the ratio of the new area to the original area when you take half of a circle's area?

• 2:1

• 1:1

• 1:2

• 3:1

How do you calculate one-fourth of a circle's area?

• Multiply by 4

• Divide by 4

• Add 4

• Multiply by 2

What is the algebraic expression for the area of a semi-circle?

• πd

• 2πr

• πr²/4

• πr²/2

What is the area of one-fourth of a square with an original area of 144 cm²?

• 36 cm²

• 72 cm²

• 18 cm²

• 144 cm²