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Math 1201 Date:______________________
1. 6 Surface Area and Volume of a Sphere
Sphere - a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. What are some real life examples of spheres? Surface Area of a Sphere The following video shows how the surface area of a sphere is equal to four times the surface area of circle with equivalent circumference. https://www.youtube.com/watch?v=FB-acn7d0zU So the surface area of a sphere is: 𝑆𝐴 = 4 𝜋𝑟^2 Example 1: Calculate the surface area to the nearest square cm.
Example 2: A sphere has a surface area of 80 in^2. Determine the diameter to the nearest inch. Example 3: An official basketball has a radius of 12.5 cm and usually has a leather covering. Approximately how much leather, in cm^2 , is required to cover 12 official basketballs?
Example 6 : A carnival clown has 75 m^3 of helium compressed in a tank. How many spherical balloons with a radius of 0.25 m can be filled with the helium from the tank? Example 7: Eight basketballs are put in a container. The radius of each basketball is 10 cm. If the container is shaped like a square based pyramid, approximately how much space not occupied by basketballs will be left if each side of the base measures 40 cm and the height is 70 cm?
Example 8: A spherical Christmas ornament measures 12 cm in circumference. What is the approximate volume of the cubed box that will hold this ornament? Example 9: A heavy sphere with diameter 20 cm is dropped into a right circular cylinder with a base radius of 10 cm and a height of 34 cm. (A) If the cylinder is half full of water, what is the total volume of the water and the sphere? (B) How high will the water rise once the sphere is completely under the water? Note: Once the sphere is dropped into the water, the water level will rise to a height that represents the volume of the water plus the volume of the sphere. Textbook Questions: page 50 - 52 # 3 , 4 , 5 , 7 , 8 , 9 , 1 0 , 1 2, 15, 1 9
