Exploring Surface Area of Spheres

The video tutorial covers the geometry of spheres, including their properties, surface area calculations, and Archimedes' discovery of the relationship between spheres and cylinders. It explains how to calculate the surface area of spheres and hemispheres, and provides examples of complex shapes like a hemisphere on a cylinder.

What is the 3D counterpart of a circle?

• Sphere

• Rectangle

• Triangle

• Square

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

• pi r^2

• 6 pi r^2

• 2 pi r^2

• 4 pi r^2

If the diameter of a sphere is 32 units, what is its radius?

• 8 units

• 32 units

• 16 units

• 64 units

How is the surface area of a sphere related to a cylinder?

• It is equal to the base area of the cylinder

• It is twice the lateral area of the cylinder

• It is equal to the lateral area of the cylinder

• None of the above

What is the surface area of a sphere if the area of its great circle is 81 pi square feet?

• 648 pi square feet

• 324 pi square feet

• 162 pi square feet

• 81 pi square feet

What additional area is considered when calculating the surface area of a hemisphere?

• The base area

• The lateral area

• The volume

• The total height

What is the total surface area of a hemisphere if the radius of its great circle is 8 yards?

• 64 pi square yards

• 256 pi square yards

• 96 pi square yards

• 192 pi square yards

How do you calculate the radius of a sphere from its surface area?

• Divide the surface area by 4 pi and take the square root

• Multiply the surface area by pi and take the square root

• None of the above

• Divide the surface area by pi and take the square root

What part of the hemisphere do you exclude when it is placed on top of a cylinder?

• The lateral area

• The base area

• The bottom area

• The top area

What is the total surface area of a composite shape consisting of a hemisphere with a radius of 5 units and a cylinder with a height of 6 units?

• 200 pi square units

• 65 pi square units

• 270 pi square units

• 135 pi square units