Humans must measure how much paint or carpet will you need to redecorate your bedroom? How many litres of water will it take to fi ll the new pool? How far is it to the end of the universe? These are just a few examples of where measurements skills are needed. Measuring tools have advanced signifi cantly in their capacity to measure extremely small and extremely large amounts, leading to many breakthroughs in medicine, engineering, science, architecture and astronomy.

Cube, cuboid and cylinder are three dimensional shapes having circular or rectangular faces. A cube or a cuboid has six faces and eight vertices on the other hand a cylinder has two circular faces joined by a curved surface. The area of all the faces of a cube is same as they are all squares.

The surface area of the can is found by adding the areas of the two circular bases and the rectangular side that surrounds them. The width, w, of the rectangle is the height of the can. The length, l, of the rectangle is equal to the circumference of the circle.

For Example:

Total surface area of a cube = 6 × (area of each side)

= 6 × a^{2} = 6 a^{2}

Similarly, total surface area of a cuboid of length ‘l’, breadth ‘b’, height ‘h’ can be calculated as,

Total surface area of a cuboid = 2 × (area of three symmetrical faces)

= 2 × (lb + bh+ hl)

Curved surface of cylinder, if opened along the diameter (d=2r) of the circular base can be transformed into a rectangle of length ‘2𝝿r’ and height ‘h’.

Thus,

Curved surface area of a cylinder of base radius ‘r’, and height ‘h’ = 2𝝿 × r × h

Total surface area of a cylinder of base radius ‘r’, and height ‘h’ = 2𝝿 × r × h + area of two circular bases

= 2𝝿 × r × h + 2𝝿r^{2}

##### __Problems related to surface area of cube, cuboid and cylinders:__

__Question:__ Calculate the cost required to paint an aquarium which is in cuboidal shape having dimensions 12m×10m×15m. If painting cost of aquarium is INR 2.5/m^{2}.

Solution: Total surface area of aquarium = 2 × (lb + bh+ hl)

= 2 × (120+ 150+ 180)

= 2 × 450 = 900 m^{2}

Total cost of painting the aquarium = 2.5 × 900 = Rs. 2250

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