Surface area and volume
What is Surface Area of Solid Figures
Surface Area of any solid is the sum of the area of all its faces.
Surface Area of Cuboid
Surface Area of cuboid = 2(lb + lh + bh)
Where l= length, b = breadth and h = height of the cuboid.
Area of four walls of Cuboid
Area of four walls of Cuboid = 2 (lh + bh) = 2h(l +b)
Surface Area of Cube
Surface area of a cube of side 'a' = 6a2
Also, lateral surface area of cube = 4a2
What is Volume
The amount of space occupied by a three - dimensional object is called its volume.
Volume of Cuboid
Volume of cuboid = l x b x h
Where l= length, b = breadth and h = height of the cuboid.
Volume of cube
A cube is a cuboid in which length, breadth and height are all equal.
Therefore, substituting l = b= h with a in the volume of cuboid formula, we get
Volume of a cube = l x b x h = a3
Volume of a cube of edge 'a' units = a3
Sums
Q1. A hall 8 m long, 6 m wide and 4 m high has three doors of size 1.5 m by 2m and four windows of size 1.2 m by 1 m. Find the cost of papering the walls if the wall paper is 80 cm wide and costs Rs. 6 per meter.
Solution :- here l = 8 m, b = 6m and h =4m
Therefore, the area of the walls of the hall
= lateral surface area
= 2h(l + b) = 2 x 4(8 + 6) m2
= 112 m2
The area of three doors
= 3 (1.5 x 2) m2 = 9 m2
The area of four windows
= 4 x (1.2 x 1)m2 = 4.8 m2
Therefore the area to be papered
= [112 - (9 + 4.8)] m2
= [112 - 13.8] m2 = 98.2 m2
The width of the paper = 80 cm = 0.8 m
Therefore the length of paper required = 98.2 / 0.8 m = 122.75 m
The cost of papering the walls = Rs. 6 x 122.75 =Rs. 736.5
Surface Area of any solid is the sum of the area of all its faces.
Surface Area of Cuboid
Surface Area of cuboid = 2(lb + lh + bh)
Where l= length, b = breadth and h = height of the cuboid.
Area of four walls of Cuboid
Area of four walls of Cuboid = 2 (lh + bh) = 2h(l +b)
Surface Area of Cube
Surface area of a cube of side 'a' = 6a2
Also, lateral surface area of cube = 4a2
What is Volume
The amount of space occupied by a three - dimensional object is called its volume.
Volume of Cuboid
Volume of cuboid = l x b x h
Where l= length, b = breadth and h = height of the cuboid.
Volume of cube
A cube is a cuboid in which length, breadth and height are all equal.
Therefore, substituting l = b= h with a in the volume of cuboid formula, we get
Volume of a cube = l x b x h = a3
Volume of a cube of edge 'a' units = a3
Sums
Q1. A hall 8 m long, 6 m wide and 4 m high has three doors of size 1.5 m by 2m and four windows of size 1.2 m by 1 m. Find the cost of papering the walls if the wall paper is 80 cm wide and costs Rs. 6 per meter.
Solution :- here l = 8 m, b = 6m and h =4m
Therefore, the area of the walls of the hall
= lateral surface area
= 2h(l + b) = 2 x 4(8 + 6) m2
= 112 m2
The area of three doors
= 3 (1.5 x 2) m2 = 9 m2
The area of four windows
= 4 x (1.2 x 1)m2 = 4.8 m2
Therefore the area to be papered
= [112 - (9 + 4.8)] m2
= [112 - 13.8] m2 = 98.2 m2
The width of the paper = 80 cm = 0.8 m
Therefore the length of paper required = 98.2 / 0.8 m = 122.75 m
The cost of papering the walls = Rs. 6 x 122.75 =Rs. 736.5