Volume Calculations of Cylinders, Cones, and Spheres

This video tutorial covers the calculation of volumes for cylinders, cones, and spheres. It begins with an introduction to the concepts and formulas for each shape, followed by detailed examples and practice problems. The tutorial also includes real-world applications, such as calculating the volume of a cone-shaped paper cup. Key formulas include the volume of a cylinder (πr²h), a cone (1/3πr²h), and a sphere (4/3πr³). The video emphasizes rounding results to the nearest tenth and provides step-by-step instructions for using a calculator.

What is the formula to calculate the volume of a cylinder?

• V = πr^2h

• V = 2πrh

• V = πr^3

• V = 1/3πr^2h

If a cylinder has a radius of 5 cm and a height of 8.3 cm, what is the volume rounded to the nearest tenth?

• 651.9 cm^3

• 415.8 cm^3

• 1303.8 cm^3

• 325.95 cm^3

How do you find the radius of a cylinder if you're given the diameter?

• Square the diameter

• Square root of the diameter

• Divide the diameter by 2

• Multiply the diameter by 2

How do you find the volume of a cylinder with a diameter of 16 inches and a height of 20 inches?

• V = π(16)^2(10)

• V = π(16)^2(20)

• V = π(8)^2(20)

• V = π(8)^2(10)

What adjustment is made to the cylinder volume formula to find the volume of a cone?

• Multiply by 1/2

• Multiply by 2/3

• Multiply by 1/3

• No adjustment is needed

What is the volume of a cone with a radius of 3 inches and a height of 6 inches, rounded to the nearest tenth?

• 56.5 in^3

• 36.5 in^3

• 18.8 in^3

• 113.1 in^3

How do you calculate the volume of a sphere?

• V = πr^3

• V = 4/3πr^3

• V = πr^2

• V = 2/3πr^3

To find the volume of a hemisphere, what should you do after finding the volume of a sphere?

• Multiply by 2

• No further action required

• Divide by 2

• Multiply by 1/3

Given a sphere with a radius of 6 mm, what is its volume rounded to the nearest tenth?

• 678.6 mm^3

• 1809.6 mm^3

• 452.4 mm^3

• 904.8 mm^3

If a cone-shaped paper cup has a height of 10 cm and a diameter of 8 cm, what is its volume rounded to the nearest tenth?

• 251.2 cm^3

• 83.8 cm^3

• 335.2 cm^3

• 167.6 cm^3