Volume
What is the formula for volume of a cylinder?
V = πr2h
What is the formula for surface area of a cylinder?
SA = 2πr2 + 2πrh
Convert 345 cm3 to mL.
345 mL
A cylinder water bottle measures 34 cm tall and 9 cm wide. It is half full of water. What is the volume of water?
V = πr2h
= 3.14(4.5)234
= 3.14(20.25)(34)
= 2161.89 cm3
HALF: 2161.89 Γ· 2 = 1080.95
There's 1080.95 mL of water.
The volume formula for most prisms does not require exponents. Why does the formula for cylinders require an exponent?
V = πr2h
This is because the volume of a prism is base x height. The formula for cylinders uses exponents, because the base is a circle, and the area of a circle requires you to square the radius.
A cylinder measures 6 cm wide and 19 cm tall.
What is the cylinder's volume?
V = πr2h
= (3.14)(3)2(19)
= (3.14)(9)(19)
= 536.94 cm3 / mL
A cylinder measures 18 cm wide and 20 cm tall.
What is its total surface area?
SA = 2πr2 + 2πrh
= (2)(3.14)(9)2 + (2)(3.14)(9)(20)
= (2)(3.14)(49) + (2)(3.14)(9)(20)
= 307.72 + 1130.4
= 1438.12 cm2
Convert 3.46 litres to mL.
3460 mL
A can of Pepsi contains 35 mL of caffeine.
How many cans of Pepsi would a person need, in order to have at least 1 litre of caffeine.
1 litre = 1000 mL
1000 Γ· 35 = 28.6
A person would need 29 cans of Pepsi, in order to have above 1 litre/1000 mL of caffeine.
Explain volume.
Volume is the amount of 3-dimensional space an object takes up.
A cylinder measures 18 m wide and 4 m tall.
What is the volume of the cylinder?
V2 = πr2h
= (3.14)(9)2(4)
= (3.14)(81)(4)
= 1017.36 m3
A cylinder has a radius of 5cm and a height of 17.5cm. What is the surface area of the cylinder?
SA = 2πr2 + 2πrh
= (2)(3.14)(5)2 + 2(3.14)(5)(17.5)
= (2)(3.14)(25) + 2(3.14)(5)(17.5)
= 157 + 549.5
= 706.5 cm2
Convert 6900 mL to litres.
6.9 litres.
Someone is wrapping cylindrical vases as special gifts. Each vase is 4 inches wide and 15 inches tall.
How much total area will need to be covered, to wrap 10 vases?
SA = 2πr2 + 2πrh
= 2(3.14)(2)2 + 2(3.14)(2)(15)
= 2(3.14)(4) + 2(3.14)(2)(15)
= 25.12 + 188.4
= 213.52
10 VASES: 213.52 x 10 = 2135.2 in2
They will need to cover a total of 2135.2 in2.
Explain how capacity can be different from volume.
Capacity refers to the maximum volume a container can hold within it.
Volume is the total 3D space that something actually takes up.
The volume inside of a container could be less than its capacity, for example if the container is partially filled.
A cylinder measures 7 cm wide and 9 cm tall.
What is the volume?
V = πr2h
= (3.14)(3.5)2(9)
= (3.14)(12.25)(9)
= 346.19 cm3
A cylinder measures 30 inches wide and 55 cm tall.
What is the surface area?
SA = 2πr2 + 2πrh
= 2(3.14)(15)2 + 2(3.14)(15)(55)
= 1413 + 5181
= 6594 cm2
Convert 4 litres cm3.
4000 cm3
A roll of toilet paper measures 16 cm wide and 9 cm tall. In the centre there is the 4 cm wide cardboard tube, filled with empty space.
What is the volume of toilet paper?
Total V = πr2h
= 3.14(8)2(9)
= 3.14(64)(9)
= 1808.64cm3
Empty space V = 3.14(2)2(9)
= 3.14(4)(9)
= 113.04cm3
Total - Empty space: 1808.64 - 113.04
= 1695.6 cm3
There is 1695.6 cm3 of toilet paper on the roll.
Explain surface area.
Surface area refers to the total 2-dimensional space covering the outside of a 3D shape. It combines the areas of each of its surfaces/faces.
A cylinder's volume is 923.16 mL, and it is 14 cm wide.
How tall is the cylinder?
V = πr2h
923.16 = (3.14)(7)2h
923.16 = (3.14)(49)h
923.16 Γ· 3.14 = 49h
294 Γ· 49 = h
6 = h
The height of the cylinder if 6 cm.
A cylinder is 12 inches wide and 10 inches tall.
What is the surface area of just the base circles (top and bottom)?
SA = 2πr2 + 2πrh
For just the area of the 2 circles.
2πr2
= 2(3.14)(6)2
= 2(3.14)(36)
= 226.08 cm2
Convert 0.025 litres to mL.
25 mL
A soup can label goes only around the curved edge of the can. One company sells cans that are 10 cm tall and 5 cm wide.
How much area will their labels cover in total, in a box of 150 soup cans?
SA = 2πr2 + 2πrh
Curved edge/rectangle part: 2πrh
= 2(3.14)(2.5)(10)
= 157
150 cans: 150 x 157 = 23,550 cm2
The total area for the labels to cover is 23 550 cm2.
Explain why we say "cubed" to represent volume.
If the unit is cm3 then the volume is a representation of how many cubes measuring 1cm x 1cm x 1cm make up the total amount of space being measured.