Exploring Volume and Surface Area of Spheres and Hemispheres

This lesson covers the geometry of spheres and hemispheres, including their definitions, properties, and formulas for calculating volume and surface area. The teacher explains the concepts of radius, diameter, and great circles, and provides step-by-step examples of how to calculate the volume and surface area for both spheres and hemispheres. The lesson emphasizes understanding the formulas and applying them to solve problems.

What is a sphere?

• A flat surface in three dimensions

• A solid where all surface points are equidistant from the center

• A circular object without depth

• A 2D shape with all points at equal distance from the center

What does the radius of a sphere represent?

• The total area of the sphere's surface

• The distance from the center to any point on the surface

• The distance across the sphere through the center

• The length around the sphere

How do you calculate the volume of a sphere?

• 2/3 pi r cubed

• pi r squared

• 4/3 pi r squared

• 4/3 pi r cubed

What is the formula for the surface area of a sphere?

• pi r squared

• 2 pi r squared

• 4 pi r cubed

• 4 pi r squared

If the diameter of a sphere is 24 mm, what is the radius?

• 48 mm

• 12 mm

• 6 mm

• 24 mm

What happens to the volume of a sphere if the radius is doubled?

• It increases eightfold

• It quadruples

• It doubles

• It stays the same

What is the volume formula for a hemisphere?

• 4/3 pi r cubed

• 3/2 pi r cubed

• 2/3 pi r cubed

• pi r cubed

How is the surface area of a hemisphere calculated?

• 2 pi r squared

• 4 pi r squared

• 3 pi r squared

• pi r squared

For a hemisphere with a radius of 5 km, what is the volume?

• 375/3 pi km^3

• 500/3 pi km^3

• 125/3 pi km^3

• 250/3 pi km^3

What additional surface does a hemisphere have compared to a sphere?

• A square

• A great circle

• A small circle

• A triangle