3.4c:surface area and volume of spheres m(g&m)–10–6 solves problems involving perimeter,...
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3.4c:Surface Area and Volume of Spheres
M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three
GSE’s
G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.?
CCSS:
Finding the Surface Area of a Sphere
• Sphere- all of the points in space that are the same distance from a point.
How is this different from a circle?
Finding the Surface Area of a Sphere
• A chord of a sphere is a segment whose endpoints are on the sphere.
Finding the Surface Area of a Sphere
• Find the surface area. When the radius doubles, does the surface area double?
S = 4r2
= 422
= 16 in.2
S = 4r2
= 442
= 64 in.2
The surface area of the sphere in part (b) is four times greater than the surface area of the sphere in part (a) because 16 • 4 = 64
So, when the radius of a sphere doubles, the surface area DOES NOT double.
More . . .
• If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a great circle of the sphere. Every great circle of a sphere separates a sphere into two congruent halves called hemispheres.
Ex. 2: Using a Great Circle
• The circumference of a great circle of a sphere is 13.8 feet. What is the surface area of the sphere?
Solution:
Using a radius of 6.9 feet, the surface area is:
S = 4r2
= 4(6.9)2
= 190.44 ft.2
So, the surface area of the sphere is 190.44 ft.2
The circumference of the cone is 3 inches
The cone is completely packed with Ice cream, and there is exactly half a scoop on top.
Find how much ice cream you will receive.