Circle and Rectangle Geometry Problems

The video tutorial covers four main geometry problems. It starts with calculating the perimeter of a rectangle given its area and side relationships. Next, it explains how to find the area of a shaded region in a circle by subtracting the area of a triangle from the circle's area. The third problem involves determining the length of a segment using midpoint and length relationships. Finally, the tutorial demonstrates how to calculate the number of cups that can be filled from a cylindrical tank by determining its volume.

What is the width of a rectangle if its length is 7 more than its width and the area is 120?

• 12

• 10

• 8

• 5

How do you calculate the perimeter of a rectangle if you know its length and width?

• Multiply the length by the width

• Add the length and width

• Multiply the length by two

• Add twice the length and twice the width

If the circumference of a circle is 16π, what is the radius?

• 32

• 4

• 8

• 16

What is the formula for the area of a circle?

• 2πr²

• πr²

• 2πr

• πr

How do you find the area of a shaded region in a circle with an inscribed triangle?

• Divide the area of the circle by the area of the triangle

• Subtract the area of the triangle from the area of the circle

• Add the area of the triangle to the area of the circle

• Multiply the area of the triangle by the area of the circle

If segment AB is 50% longer than segment BC, and BC is 2y, what is the length of AB?

• y

• 3y

• 2y

• 4y

What is the length of segment BD if BC is 8 and CD is 20?

• 30

• 28

• 20

• 18

What is the formula for the volume of a cylinder?

• 2πrh

• πr²h

• 2πr²

• πr²

If a cylindrical tank has a diameter of 16 inches, what is its radius?

• 8 inches

• 16 inches

• 12 inches

• 4 inches

How many cups can be filled from a cylindrical tank if the volume of the tank is 4825.486 cubic inches and each cup holds 134 cubic inches?

• 34

• 37

• 35

• 36