Cubes
A cube is a special type of cuboid where each of the six faces are squares.
The volume of a cube = length3
This means length 脳 length 脳 length
The surface area of a cube = 6 脳 area of one square
Question
Calculate the volume and surface area of this puzzle cube that measures 3 inches in height.
Volume:
3 脳 3 脳 3 = 33 = 27 inches3
Surface area:
Area of one square = 3 脳 3 = 9 inches2
Total surface area = 6 脳 9 inches2 = 54 inches2
Question
A 6 m cube tank is full of water. An empty tank the shape of a cuboid has a base of length 10 m and width 8 m. The water is transferred from one tank to the other. Calculate the height of the water in the new tank.
\(\text{Volume = width} \times \text{length} \times \text{height}\)
1. Calculate the volume of the water in the cube-shaped tank:
Volume = 6 m 脳 6 m 脳 6 m = 216 m3
2. To calculate the volume of the water in the cuboid-shaped tank, substitute in the known values:
216 = 8 脳 10 脳 height
216 = 80 脳 height
3. Rearrange the equation to calculate the height:
Height = 216 梅 80
Height = 2.7 m
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