Volume of Spheres and Cylinders

This video tutorial covers Math 8 Unit 5 Lesson 21, focusing on calculating the volumes of cylinders, cones, and spheres. It includes a detailed explanation of volume formulas, a class activity involving problem-solving with partners, and several example problems. The lesson also explores practical applications, such as determining the volume of a cylinder tank and when a sensor alerts for low water levels. Students will learn to calculate volumes, understand the relationships between different shapes, and apply these concepts to real-world scenarios.

What is the correct volume of a sphere with a radius of 9 cm?

• 972π

• 972

• 108π

• 108

If the volume of a sphere is 288π, what is the radius?

• 5

• 4

• 7

• 6

What is the volume of a cylinder with a radius of 1.5 cm and height of 8 cm?

• 30π

• 24π

• 18π

• 12π

Which shape cannot hold 18π cm³ of water?

• Sphere

• Rectangular Prism

• Cylinder

• Cone

How tall should an ice cream cone be to hold a scoop with a 3-inch radius?

• 6 inches

• 9 inches

• 12 inches

• 15 inches

What is the volume of a sphere with a diameter of 6 inches?

• 108π in³

• 72π in³

• 54π in³

• 36π in³

What is the volume of a cylinder with a height of 6 inches and a diameter of 6 inches?

• 72π in³

• 108π in³

• 54π in³

• 144π in³

What proportion of a large sphere's volume is occupied by smaller spheres if there are 243 of them?

• 66%

• 50%

• 33%

• 25%

What is the volume of a cylinder with a radius of 7 and height of 3?

• 615.44

• 461.58

• 294π

• 154π

At what volume will the sensor alert the farmer to refill the tank?

• 184.632

• 92.316

• 230.79

• 461.58