## Wednesday, January 26, 2011

### Questions 15 and 16

Question 15:

a) If the edge length of a cube is doubled, find the ratio of the old surface area to the new surface area.
b) What happens if the edge length of a cube is tripled? Is there a pattern?

a) 1:4. Instead of thinking of it as a cube, I thought of it as a square. Let's say a side of a cube's side lengths were 6m and had an area of 36cm2. You multiply the side lengths by 2, which becomes 12, and find the new area which is 144. 144/36=4. So, the ratio is 1:4.

b) If the side length is tripled, the new ratio becomes 1:9. There is a pattern if you continue doing this. All of the lengths are prime numbers while the other numbers stay the same. For example, 1:4, 1:9, 1:16, 1:25. ( x 4=64)

Question 16:

Shelby wants to paint the walls and ceiling of a rectangular room. 1 liter of paint covers 9.5 m2.

a) What is the least amount of paint Shelby can buy to paint the room (subtract 5 m2

for the door and windows)?
b) How much will the paint cost, including the amount of tax charged in your region?

The height is 2.6m2, the length is 4.8m2, the width is 6.8m2. 1 liter of paint covers 9.5 m2.

a) L x W
2.6 x 4.8
2.6 x 4.8
2.6 x 6.8
2.6 x 6.8
6.8 x 4.8
6.8 x 4.8=
125.6 125.6-5= 120.6
120.6-65.28 (the ceiling paint has to be separated from the wall paint)= 55.32
55.32/9.5=5.8

Wall paint: 1 can 4L, 2 cans 1L.
Ceiling paint: 1 can 4L.

b) The cost will be 82.75 with 12% GST and PST.

Wall paint: 4L= \$24.95
1L=\$7.99
Ceiling paint: 4L=\$32.95

24.95+7.99+7.99+32.95=73.88
12%= 8.87.
73.88+8.87= 87.75

Cylinder Volume and Volume Problems

a) (π x r x r) x h
(3.14 x 5 x 5)x 8
78.5 cm2 x 8cm
volume=628cm3

b) (π x r x r) x h
(3.14 x 11 x 11) x 11
379.94 x 11
v=4179.34cm3

c)(π x r x r) x h
(3.14 x 1.1 x 1.1) x 2.6
3.7994 x 2.6
v=9.87844cm3

d) (π x r x r) x h
(3.14 x 4.5 x 4.5) x 25
56.52 x 25
v=1413cm3

with inside diameter:
(π x r x r) x h
(3.14 x 4 x 4) x 40
50.24 x 40
v=2009.6cm3

with outside diameter:
(π x r x r) x h
(3.14 x 5 x 5) x 40
78.5 x 40
v=3140cm3

3140-2009.6= 1130.4

capacity of pipe 1130.4cm3