## Friday, February 4, 2011

### Raelynn's Surface Area Scribe

Math Textbook Pages 185-186. Show you knows and Questions 1,3,5.

Show you know #1:
Calculate the surface area of a cylindrical waste bucket without a lid that measures 28 cm high and 18 cm in diameter. Give your answer to the nearest square centimeter.

TSA= (2π.r.r) + (2.r.π.h)
TSA= (2x3.14x9x9) + (2x9x3.14x28)
TSA= 508.68 + 1582.56
TSA= 2091.24cm²

Show you know #2:
Calculate the surface area of this cylinder to the nearest tenth of a square centimeter.
Diameter: 9 cm
Height: 55 cm

TSA= (2π.r.r) + (2.r.π.h)
TSA= (2x3.14x4.5x4.5) + (2x4.5x3.14x55)
TSA= 127.17 + 1554.3
TSA= 1681.47cm²

1. What are the similarities and differences between finding the surface area of a prism and finding the surface area of a cylinder?
Differences: The surface area of a prism is that it is rectangular. It has 6 faces. A cylinder has a total of three surfaces: a top, bottom, and middle. The top and bottom, which are circles.
Similarities: They both have nets to identify the answer. They are also easy to visualize.

3. a) Draw a net for this cylinder.
b) Sketch a different net for this cylinder.

5. Find the surface area of each object to the nearest tenth of a square unit.

a)
Diameter: 2.5 cm

Circumference: 16 cm
b)Diameter: 0.003 m
Circumference: 16 m
a)
TSA= (2π.r.r) + (2.r.π.h)
TSA= (2x3.14x1.25x1.25) + (2x1.25x3.14x16)
TSA= 9.8125 + 125.6
TSA= 135.4cm²
b)
TSA= (2π.r.r) + (2.r.π.h)
TSA= (2x3.14x0.0015x0.0015) + (2x0.0015x3.14x16)
TSA=0.00001413 + 0.15072
TSA= 0.2cm²

Cylinder Volume and Volume Problems

Jumbo
v= π.r.r.h
v= (3.14x10x10) x 40
v= 314 x 40
v= 12560cm3

Popcorn Lover's
v= π.r.r.h
v= (3.14x15x15) x 20
v= 706.5 x 20
v= 14130cm3

Martha should buy the container that says "Popcorn Lover's" if she wants more popcorn for her money.

Outside
r=d/2
r=1/2
r=0.5

v= π.r.r.h
v= (3.14x0.5x0.5x10)
v= (0.785m2) x 10m
v= 7.85m3

Inside
v= π.r.r.h
v= (3.14x0.4x0.4x10)
v= (0.5024m2) x 10m
v= 5.024m3

7.85cm3 - 5.024m3 = 2.862 or 2.9m3

The volume of the concrete required to make the culvert is 2.9m3.