Week 6 Wednesday: surface area of spheres, cones, and pyramids
KEY
Warm-ups: (Feel free to use a calculator and the formula sheet.)
1) a. Find the formula for the surface area of a sphere, and write it here:
b. To the nearest square meter, what’s the surface area of a sphere with radius 8.2 m?
SA = 4  r2
SA  4 (3.14) (8.22)
SA  844.5344
SA rounded to nearest square meter is
845 m2
2) a. Find the formula for the surface area of a cone, and write it here:
b. Remember that the net of a cone has 2 parts—the circle that is the base, and the
triangle -like part with the curvy bottom that forms the curved face of a cone.
Which part of the formula do you think goes to each part of the net?
c. The variable “s” in the formula means slant height. On the picture of the cone below,
indicate where you think slant height might be.
D. Stark 5/2/2016
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3) a. Find the formula for the surface area of a pyramid, and write it here:
Also write the formula for the surface area of a right prism:
You don’t have to write anything down, but just take a moment to notice how these formulas are
similar and different. See how they both use the perimeter (p) of the Base. Look at the number
of Bases (B) in the formulas and whether the height is regular height (h) or slant height (s).
Prisms sit straight up so the formula uses height (h), and there are 2 bases (B).
Pyramids are slanted so the formula uses slant height (s), which is the actual height of the
triangular face. There’s only one base (B) on a pyramid. The ½ times the perimeter times
the slant height is just a quick way of getting the area of all the triangles that are the lateral
faces. (The area of a triangle is ½ bh.)
As an alternative to using the formula, for the surface area of a pyramid you could just add
B to the area of each of the lateral face triangles.
straight math handouts: surface area of spheres/ surface area of cones/ surface area of square pyramids
extra straight math practice: surface area of mixed shapes
story problems: Scoreboost M&G p. 27 #1, 4, 5
D. Stark 5/2/2016
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