Surface area and volume
Class 8
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