Title Class 9 Mathematics Chapter 13 Surface Areas and Volume.pdf ✅

Surface Areas and Volumes DPP-01 [Topic: Surface Area of a Cuboid and a Cube] Very Short Answer Type Questions 1. Find the length of the longest rod that can be put in a hall of dimension 23m × 10m × 10m, 2. Find the length of the longest rod that can be fitted in a cubical vessel of edge 10cm long. 3. If the length of a diagonal of a cube is 8√3cm, then find its surface area. 4. If each edge of a cuboid of surface area SS is doubled, what will happen to surface area of the new cuboid? 5. Find the surface area of a chalk-box whose length, breadth and height are 16cm, 8cm and 6cm respectively. 6. Find the lateral surface area of a cube whose edge is 11cm. 7. The perimeter of one face of a cube is 40cm. Find the sum of lengths of its edges. 8. If length is ll, breadth is bb and height is h, then find the total surface area of a cuboidal vessel which is open at the top. 9. The total surface area of a cube is 726cm2. Find the length of its edge. Short Answer Type Questions-I 10. Find the lateral surface area of a cube, if length of its diagonal is 6√3m. 11. Three cubes each of side 4cm are joined end- to-end. Find the surface area of the resulting cuboid. 12. Two cubes each of 5cm edge are joined end- to-end. Find the surface area of the resulting cuboid. 13. Find the cost of white-washing the four walls of a room with dimensions 5m × 4m × 3m at the rate of ₹ 12 per m2. Short Answer Type Questions-II 14. The length, breadth and height of a solid cuboid are in the ratio 5: 4: 2. If the total surface area is 1216 cm2, find the dimensions of the cuboid. 15. If each edge of a cube is increased by 50%, find the percentage increase in the surface area, 16. The length, breadth and height of a room are 4m, 3m and 7m respectively. Find the cost of white-washing the walls of the room and the ceiling at the rate of ₹6 per m2. 17. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25cm wide and 25cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?
Long Answer Type Questions 18. The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm × 10cm × 7.5cm can be painted out of this container? 19. A cubical box has each edge 10cm and another cuboidal box is 12.5cm long, 10cm wide and 8cm high. (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much? 20. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5m, with base dimenions 4m × 3m ? 21. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25cm × 20cm × 5cm and the smaller of dimensions 15cm × 12cm × 5cm. For all the overlaps 5% of the total surface area is required extra. If the cost of the cardboard is ₹4 for 1000cm2, find the cost of cardboard required for supplying 250 boxes of each kind. 22. A wooden bookshelf has external dimensions as follows: Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2, and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
Surface Areas and Volumes DPP-02 [Topic: Volume of aCuboid and a Cube] Very Short Answer Type Questions 1. If the volumes of two cubes are in the ratio 8: 1, then find the ratio of their edges. 2. If each edge of a cube, of volume V is doubled, then find the volume of the new cube. 3. Volume of a cuboid is 12cm3. Find the volume (in cm3 ) of a cuboid whose sides are double of the above cuboid. 4. Find the number of cubes of side 3cm that can be cut from a cuboid of dimensions 10cm × 9cm × 6cm. 5. The lateral surface area of a cube is 100m2. Find the volume of the cube. 6. The total surface area of a cube is 150cm2. Find the volume of the cube, 7. Find the number of plants of dimensions (4m × 50cm × 20cm) that can be stored in a pit which is 16 m long, 12m wide and 4m deep. 8. If the volume of a cube is 3√3aa3, then find its total surface area. 9. The diagonal of a cube is √12cm, Find its volume. 10. Write the edge of cube in terms of its volume. 11. If the total surface area of a cube is 96cm2, then find its volume. 12. Find the number of small cubes with edge 20cm that can be accommodated in a cubical box of 2 metres edge. Short Answer Type Questions-I 13. If the volume of a cuboid is 440cm3 and the area of base is 88cm2, find the height of the cuboid. 14. A cuboidal water tank is 8m long, 4m wide and 7m deep. How many litres of water can it hold? 15. A cuboidal block of wood is of dimensions 5m × 2m × 1m. Find the number of cubes of dimensions 1 m × 1m × 1m which can be cut from it. 16. A metallic sheet is of the rectangular shape with dimensions 48cm × 36cm. From each one of its corner, a square of 8cm is cut off. An open box is made of the remaining sheet. Find the volume of the box, 17. A cuboidal vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic metres of a liquid? Short Answer Type Questions-II