Surface Area and volume ClassVIII By S M

Surface Area and volume Class-VIII By S M Rahman

Surface Area and Volume

Cube and Cuboid • • Diagonal of a cube = √ 3 x edge(l) Perimeter of a cube = 12 x edge Diagonal of a cuboid = Perimeter of a Cuboid = 4(l + b +h)

Cube • Surface Area of a Cube: For cube, length = breadth = height Suppose the length of an edge = l Hence, surface area of the cube = 2(l × l + l × l) = 2 x 3 l 2 = 6 l 2 Total Surface Area of Cube= 6 l 2 • Lateral surface area of a Cube: Formula to find Lateral surface area of the cube is: 2(l × l + l × l) = 4 l 2 LSA of Cube = 4 l 2 • Volume of the Cube: • The volume of the cube is equal to the product of the area of the cube and height. As we know already, all the edges of the cube are of the same length. Hence, Volume of the cube = l 2 × h Since, l = h • Volume of the cube = l 2 × l = l 3

Questions on cube 1. Example: If the length of the side of the cube is 6 cm, then find its total surface area? Given, side length = 6 cm TSA of cube = 6 l 2 TSA = 6 (6)2 = 6 x 36 TSA = 216 sq. cm 2. If the length of the side of the cube is 6 cm, then find its lateral surface area? • Given, Side length, l = 6 cm • LSA of cube = 4 l 2 = 4 (6)2 • LSA = 4 x 36 = 144 sq. cm 3. If the length of the side of the cube is 6 cm, then find its Volume? • Given, side length = 6 cm • Volume of cube = side 3 = 63 = 216 cubic. cm

Cuboid Consider a cuboid having the length to be ‘l’ cm, breadth be ‘b’ cm and height be ‘h’ cm. Area of face EFGH = Area of Face ABCD = (l× b) cm 2 Area of face BFGC = Area of face AEHD = (b ×h) cm 2 Area of face DHGC = Area of face ABFE = (l ×h) cm 2 Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces = 2(lb + bh + lh)

Questions on Cuboid • • Example 1: Find the total surface area of the cuboid with dimensions 2 inches × 3 inches × 7 inches? Solution: Total Surface Area(TSA) = 2 (lb + bh + hl ) TSA = 2 ( 2× 3 + 3× 7 + 7× 2) TSA = 2 ( 6 + 21 + 14 ) = 82 So, the total surface area of this cuboid is 82 inches 2 Example 2: The length, width and height of a cuboid are 12 cm, 13 cm and 15 cm, respectively. Find the lateral surface area of a cuboid? Solution: Lateral surface area of a cuboid is given by: LSA = 2 h ( l + w ) LSA = 2× 15 ( 12 + 13 ) = 750 cm 2

The dimensions of a cuboid are given as follows: Length = 4. 8 cm , Width = 3. 4 cm , Height = 7. 2 cm. Find the Total Surface area and the Lateral Surface area? • Solution: The total surface area is given as : TSA = 2 (lw + wh + hl) =2((4. 8 × 3. 4) + (3. 4× 7. 2) + (7. 2× 4. 8)) = 2(16. 32 +24. 48 +34. 56) = 2(75. 36) cm² Therefore, TSA of a cuboid= 150. 72 sq cm Also, the lateral surface area = 2 h (l + w) = 2× 7. 2 (4. 8 + 3. 4) = 14. 4 (8. 2) = 118. 08 Therefore, LSA of a cuboid = 118. 08 cm²

Cylinder

Volume of a Cylinder Formula • A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.

Volume of Hollow Cylinder • In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed by the base of hollow cylinder. Suppose, r 1 and r 2 are the two radii of the given hollow cylinder with ‘h’ as the height, then the volume of this cylinder can be written as; • V = πh(r 12 – r 22)

Test Zone • Find the total surface area of an open cylindrical tank of radius 4. 9 m and height 9. 5 m. How many litres of water can it hold? (Ans: 716870 litre) • Find how much wood was used in making a cubical chalk box of side 15. 8 cm and thickness 3 cm? (Ans: 3003. 12) • Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm? (Ans: 1397) • The curved surface area of a cylindrical road is 132 cm 2. Find its length if the radius is 0. 35 cm? (Ans: - 60 cm) • The area of the base of a right circular cylinder is 616 cm 2 and its height is 2. 5 cm. Find the curved surface area of the cylinder? (Ans: -220) • A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a cylinder. Find the total surface area of the cylinder thus generated? (Ans: 1188)

The End Thank you