Exploring Volume of Spheres, Cylinders, and Cones

Miss Etheridge covers pages 675-678 of the textbook, focusing on solving volume problems involving cylinders, cones, and spheres. The lesson includes calculating the volume of a cone, finding the volume of composite figures, comparing volumes of different shapes, and applying these concepts to real-world scenarios like making candles. The session emphasizes using calculators for precise calculations and understanding the relationships between different geometric shapes.

What is the formula used to calculate the volume of a cone?

• 1/3 * pi * r^2 * h

• pi * r^2 * h

• 4/3 * pi * r^3

• 2 * pi * r * h

What is the volume of a cone with a radius of 6 and a height of 5, using 3.14 for pi?

• 188.4 units^3

• 565.2 units^3

• 100 units^3

• 300 units^3

How do you find the height of a cylinder when given the total volume?

• Divide the total volume by the area of the base

• Multiply the volume of the half sphere by 2

• Add the volume of the half sphere to the total volume

• Subtract the volume of the half sphere from the total volume and solve for height

What is the relationship between the volume of a cone and a cylinder with the same radius and height?

• The volume of the cylinder is three times the volume of the cone.

• The volume of the cone is twice the volume of the cylinder.

• The volume of the cylinder is the same as the volume of the cone.

• The volume of the cone is half the volume of the cylinder.

What is the volume formula for a sphere?

• pi * r^2 * h

• 2 * pi * r^3

• 1/3 * pi * r^2 * h

• 4/3 * pi * r^3

What is the correct way to calculate the volume of a cylinder?

• pi * r^2 * h

• 4/3 * pi * r^3

• 1/3 * pi * r^2 * h

• 2 * pi * r * h

How do you calculate the volume of a half sphere?

• 1/2 * 4/3 * pi * r^3

• 2 * pi * r^3

• 4/3 * pi * r^3

• pi * r^2 * h

What is the volume of a figure made of a cone and a half sphere, using 3.14 for pi?

• 318.2 cm^3

• 500 cm^3

• 150 cm^3

• 678.24 cm^3

How many spherical candles can Geraldo make with a pitcher of wax 7 inches deep and spherical molds of diameter 4 inches?

• 5 candles

• 4 candles

• 6 candles

• 7 candles

If the volume of a sphere is given as 36 pi, what is its diameter?

• 12

• 3

• 18

• 6