Class 8: Chapter 37 Volume and Surface Area of Solids Exercise 37

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1 Class 8: Chapter 37 Volume and Surface Area of Solids Exercise Find the volume, the total surface area and the lateral surface area of the cuboid having: a. Length (l) = 24 cm, breadth(b) = 16 cm and height(h) = 7.5 cm b. Length (l) = 10 m, breadth(b) = 35 cm and height(h) = 1.2 m a) Volume of a cuboid = (l b h) = = 2880 cm 3 Total surface Area of a cuboid = 2(lb + bh + lh) = 2( ) cm 2 = 1368 cm 2 Lateral surface Area of a cuboid = 2(l + b) h = 2( ) 7.5 cm 2 = 600 cm 2 b) Volume of a cuboid = (l b h) = = 4.2 m 3 Total surface Area of a cuboid = 2(lb + bh + lh) = 2( ) cm 2 = m 2 Lateral surface Area of a cuboid = 2(l + b) h = 2( ) 1.2 cm 2 = m 2 2. Find the capacity of a rectangular tub whose length = 6 m, breadth = 2.5 m and depth 1.4 m. Also find the area of the iron sheet required to make the tub. Volume of the tub = (l b h) = = 21 m 3 Total surface Area of a cuboid = 2(lb + bh + lh) = 2( ) m 2 = 53.8 m 2 3. A wall of length 13.5 m, width 60 cm and height 1.6 m is to be constructed by using bricks of dimensions 22.5 cm by 12 cm by 8 cm. How many bricks would be needed. Volume of the wall = (l b h) = = m 3 Volume of the brick = (l b h) = = m 3 Volume of the wall Number of bricks needed = Volume of the brick = =

2 4. How many planks each measuring 5 m by 24 cm by 10 cm can be stored in a place 15 m long, 4 m wide and 60 cm deep? Volume of the place = (l b h) = = 36 m 3 Volume of the plank = (l b h) = = 0.12 m 3 Volume of the place Number of planks stored = Volume of the plank = = A classroom is 10 m long, 6.4 m broad and 5 m height. If each student is given 1.6 m 2 of the floor area, how many students can be accommodated in the room? How many cubic meters of air would each student get? Area of the floor of the classroom (l b) = = 64 m 2 Area given to each student = 1.6 m 2 Number of students that can be accommodated in the room = = 40 Cubic meters of air would each student get = 1.6 m 2 5m = 8m 3 6. Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad and 9 m high. Diagonal of a cuboid = = 17m = longest pole that can be placed in the room 7. The volume of the cuboid is 972 m 3. If its length and breadth be 16 m and 13.5 m respectively, find its height. Volume of a cuboid = (l b h) 972 = h h = 4.5m 8. The volume of the cuboid is 1296 m 3. Its length is 24 m and its breadth and height Are in the ratio of 3: 2. Find the breadth and height of the cube. Volume of a cuboid = (l b h) 1296 = 24 3x 2x x = 3 m Breadth = 9 m and Height is 6 m 2

3 9. The surface area of the cuboid is 468 cm 2. Its length and breadth are 12cm and 9 cm respectively. Find its height. Surface Area of a cuboid = 2(lb + bh + lh) 468 = 2( h + h 12) h = 6 m 10. The length, breadth and height of the room are 8 m, 6.5 m and 3.5 m respectively. Find: i) the area of the four walls of the room ii)the area of the floor of the room l = 8m, b = 6.5 m, h = 3.5m i) Area of four walls would be = (l h + b h) 2 = ( ) 2 = m 2 ii) The area of the floor of the room = l b = = 52 m A room 9 m long, 6 m wide and 3.6 m high has one door 1.4 m by 2 m and two windows each 1.6 m by 75 cm. Find the: i) area of four walls, excluding the doors and the windows. ii) cost of painting the wall from inside at a rate of Rs/m 2. iii) the cost of painting the ceiling at 25 Rs/m 2. i) Area of walls excluding the doors are windows = (l h + b h) 2 (Area of Doors) 1 (Area of Window) 2 = ( ) ( ) 2 = m 2 ii) Cost of painting the wall = = 2313 Rs. iii) Costof painting the ceiling = (9 6) 25 = 1350 Rs. 12. An assembly hall is 45 m long, 30 m broad and 16 m height. It has five doors, each measuring 4 m by 3.5 m and four windows 2.5 m by 1.6 m each. Find the i) cost of wall paper at a rate of 35Rs/m 2 ii) cost of carpeting the floor at the rate of 154 Rs/m 2. Wall dimensions: l = 45 m, b = 30 m, h = 16 m Door dimensions = 4m by 3.5 m Window dimensions = 2.5 m by 1.6 m Area of walls excluding the doors are windows = (l h + b h) 2 (Area of Doors) 5 (Area of Window) 4 = ( ) ( ) 4 = 2314 m 2 i) Cost of painting the wall = = Rs. 3

4 ii) cost of carpeting the floor = = Rs. 13. The length, breadth and height of the cuboid are in the ratio of 7: 6: 5. If the surface area of the cuboid is 1926 cm 2, find its dimensions. Also find the volume of the cuboid. Wall dimensions: l = 7x, b = 6x, h = 5x Surface Area of a cuboid = 2(lb + bh + lh) 2(42x x x 2 ) cm 2 = 1926 cm 2 x = 3 l = 21 cm, b = 18 cm and h = 15 cm Volume = = 5670 cm If the area of the three adjacent faces of a cuboidal box are 120cm 2, 72 cm 2 and 60 cm 2 respectively, then find the volume of the box. Let the dimensions: l, b, h l b = 120 b h = 72 h l = 60 Multiplying the above three expressions we get l 2 b 2 h 2 = Volume = = 720cm A river 2 m deep and 40 m wide is flowing at a rate of 4.5 km. How many cubic meters of water runs into the sea per minute? m Rate of flow = 3600 s = 1.25 m s Volume of wate flowing = = 6000 m A closed wooded box 80 cm long, 65 cm wide, and 45 cm high, is made up of wood 2.5 cm thick. Find i) the capacity of the box, ii) weight of the box if 100cm 3 of wood weighs 8 grams. External Volume of the Box = (l b h) = = cm 3 Internal Length = [80 ( )] = 75 cm Internal Breadth = [65 ( )] = 60 cm Internal Height = [45 ( )] = 40 cm hr 4

5 Internal Volume = = cm 3 Volume of Wood = = 4320 gm = 4.32 kg 17. The external dimensions of a wooden box, open at the top are 54cm by 30 cm by 16 cm. It is made up of wood 2 cm thick. Calculate i) the capacity of the box ii) the volume of the wood. External Volume of the Box = (l b h) = = cm 3 Internal Length = [54 (2 + 2)] = 50 cm Internal Breadth = [30 (2 + 2)] = 26 cm Internal Height = [16 (2)] = 14 cm Internal Volume = = cm 3 Volume of Wood = = 7720 gm = 7.72 kg 18. The internal dimension of the closed box, made up of iron 1 cm thick, are 24 cm by 18 cm by 12 cm. Find the volume of the iron in the box. Internal Volume of the Box = (l b h) = = 5184 cm 3 External Length = [24 + (1 + 1)] = 26 cm External Breadth = [18 + (1 + 1)] = 20 cm External Height = [12 + (1 + 1)] = 14 cm External Volume = = 7280 cm 3 Volume of Iron = = 2096 cm Find the volume, the total surface area and the lateral surface area and the diagonal of each cube whose edges measures: i) 8 m ii) 6.5 cm iii)2 cm 6 mm i) Volume of a cube = 8 3 = 512 m 3 Total surface Area of a cube = = 384 m 2 Lateral surface Area of a cube = = 256 m 2 ii) Diagonal of a cube = a 3 = = m Volume of a cube = (6.5) 3 = cm 3 Total surface Area of a cube = 6 (6.5) 2 = cm 2 Lateral surface Area of a cube = 4 (6.5) 2 = 169 cm 2 Diagonal of a cube = a 3 = = cm 5

6 iii) Volume of a cube = (2.6) 3 = cm 3 Total surface Area of a cube = 6 (2.6) 2 = cm 2 Lateral surface Area of a cube = 4 (2.6) 2 = cm 2 Diagonal of a cube = a 3 = = cm 20. The surface area of the cube is 1176 cm 2. Find its volume. Surface Area of a cube = 6a 2 = 1176 a = 14 Volume of cube = 14 3 = 2744 cm The volume of the cube is 216 cm 3. Find its surface area. Volume of a cube = a 3 = 216 a = 6 Surface area = = 216 cm The volume of a cube is 343 cm 3. Find its surface area. Volume of a cube = a 3 = 343 a = 7 Surface area = = 294 cm A solid piece of metal in the form of cuboid of dimensions 24 cm by 18 cm by 4 cm is melted down and re casted into a cube. Find the length of each edge of the cube. Volume of a cuboid = (l b h) = = 1728 Let the dimension of cube = a Volume of Cube = a 3 = cm 24. Three cubes of metal with edges 5 cm by 4 cm by 3 cm are melted to form a single cube. Find the lateral surface area of the new cube formed. Let the dimension of the large cube = a Volume of Large Cube = = 216 = a 3 Therefore the dimension of the large cube = 6 cm Lateral surface Area of a cube = 4 (6) 2 = 144 cm 2 6

Assignment Volume and Surface Area of Solids

Assignment Volume and Surface Area of Solids 1. (a) The diagonal of a cube is 16 3 cm. Find its surface area and volume. (b) The capacity of a cylindrical tank is 1848 m 3 and the diameter of its base