Communication
Explain the formula for volume.
Volume = Base x Height
- The base of the cylinder is a circle, so pi x r2 is the base
- Multiplying pi x r2 x h results in the total volume
Find the volume of a cylinder with a diameter of 8 metres, and a height of 18 metres.
V = pi x r2 x h
= pi x 42 x 18
= pi x 16 x 18
= 904.32 m3
Find the surface area of a cylinder with a height of 10 cm and a width of 12 cm.
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 62 x 2 + pi x 12 x 10
= pi x 36 x 2 + 376.8
= 226.08 + 376.8
= 602.88 cm2
A can of cake frosting has a diameter of 10 cm, and a height of 12 cm. How many mL of frosting do you expect to fit in this can?
Capacity/volume: V = pi x r2 x h
= pi x 52 x 12
= pi x 25 x 12
= 942 cm3
I expect there to be 942 mL of frosting.
What is "lateral area" of a cylinder?
The area of the curved surface, the rectangular shape of the cylinder net.
Explain the surface area formula.
SA = (pi x r2 x 2) + (pi x d x h)
- The pi x r2 x 2 represents the area of the 2 circles, since pi x r2 is the area of 1 circle, then multiplied by 2
- pi x d x h represents the area of the rectangle (lateral) surface
Find the volume of a cylinder with a radius of 6 cm, and a height of 15 cm.
V = pi x r2 x h
= pi x 62 x 15
= pi x 36 x 15
= 1, 695.6 cm3
or 1, 695.6 mL
or approximately 1.7 litres
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 92 x 2 + pi x 18 x 14
= pi x 81 x 2 + 791.28
= 508.68 + 791.28
= 1, 299.96 cm2
A circular hot tub has a width of 3 metres and a height of 1 metre. If the hot tub was filled to the very top with water, what is the volume of water that would be in the hot tub?
Volume = pi x r2 x h
= pi x 1.52 x 1
= 7.065 m3
I expect the volume of water in the hot tub to be 7.065 m3.
There are 6 cans of tuna, each with a diameter of 6 cm and a height of 3 cm. How much volume is in these cans altogether?
V = (pi x r2 x h) x 6 (for 6 cans)
= pi x 32 x 3 x 6
= pi x 9 x 3 x 6
= 84.78 x 6
= 508.68 cm3
There is 508.68 cm3 or 508.68 mL all together.
Explain the difference between volume and surface area.
Volume represents the total amount of 3-dimensional space occupied by a shape.
Surface area represents the total amount of exterior 2-dimensional space around the outside of a shape.
Find the volume of a cylinder with a diameter of 24 mm and a height of 80 mm.
V = pi x r2 x h
= pi x 122 x 80
= pi x 144 x 80
= 36, 172.8 mm3
Find the surface area of a cylinder with a radius of 3 inches and a height of 17 inches.
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 32 x 2 + pi x 6 x 17
= pi x 9 x 2 + 320.28
= 56.52 + 320.28
= 376.9 in2
A cylindrical candle has a height of 9 cm, and a width of 2 cm. If you had to wrap the candle in tissue paper, how much tissue paper would you need (minimum)?
Wrapping around the outside --> Surface area
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 12 x 2 + pi x 2 x 9
= pi x 1 x 2 + 56.52
= 6.28 + 56.52
= 62.8 cm2
A pool (diameter = 4 metres, and height is 3 metres) is filled to the top with water. Then, Dar jumps into the pool and a 1 m3 of water splashes out. How much water is left in the pool?
V = (pi x r2 x h) - water removed
= pi x 22 x 3 - 1
= pi x 4 x 3 - 1
= 37.68 - 1
= 36.68 m3
There is 36.68m3 still in the pool.
Convert into mL:
1.75 litres
1.75 L = 1, 750 mL
Find the volume of a cylinder with a radius of 14 m and a height of 29 m.
V = pi x r2 x h
= pi x 142 x 29
= pi x 196 x 29
= 17, 847.76 m3
Find the surface area of a cylinder with a width of 8 metres and a height of 2 metres.
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 42 x 2 + pi x 8 x 2
= pi x 16 x 2 + 50.24
= 100.48 + 50.24
= 150.72 m2
A toilet paper roll has a height of 9 cm and a width of 2 cm. If you were to wrap both the inside and outside of the tissue paper roll, how much paper would you need?
I need the rectangular area only, multiplied by 2.
(Inside and outside)
SA = (pi x d x h) x 2
= (pi x 2 x 9) x 2
= (56.52) x 2
= 113.04 cm2
You would need 113.04 cm2 of paper to wrap the inside and outside of the toilet paper roll.
Spell the word (listen to Ms. Hickey)
M E A S U R E M E N T
Convert to cm2:
4.5 km2
4.5 km2 = 4, 500 m2 = 450, 000 cm2
Find the height of a cylinder, with a diameter of 20 cm and a volume of 1, 884 cm3.
V = pi x r2 x h
1884 = pi x 102 x h
1884 = pi x 100 x h
1884 ÷ 100 = pi x h
18.84 = 3.14 x h
18.84 ÷ 3.14 = h
6 cm = h
Find the surface area of a cylinder with a radius of 7 cm and a height of 30 cm.
SA = (pi x r2 x 2) + (pi x d x h)
= pi x 72 x 2 + pi x 14 x 30
= pi x 49 x 2 + 1, 318.8
= 307.72 + 1, 318.8
= 1, 626.52 cm2
The circular swimming pool is 8 metres wide. The water is 2 metres high. How many mL are in the pool?
mL = volume
V = pi x r2 x h
= pi x 42 x 2
= 3.14 x 16 x 2
= 100.48 m3
100.48 m3 = 10, 048 cm3 = 10, 048 mL
There are 10, 048 mL of water in the pool.
Spell the word (listen to Ms. Hickey)
M A X I M U M
C A P A C I T Y