1. Find the edge of a cube of volume equal to the volume of a cuboid of dimensions 63 cm × 56 cm × 21 cm.
2. Find the number of 5 cm cubes that can be cut out of a 15 cm cube. 3. Three cubes of metals whose edges are 3, 4 and 5 cm respectively are melted and formed into a single cube. If there is no waste in the process, find the edge of the new cube so formed.
4. A school room is to be built to accommodate 70 children, so as to allow 2.2 sq m of floor area and 11 cu m of space for each child. If the room is to be 14 m long, what must be its breadth and height ?
5. How many bricks 20 cm × 10 cm × 7.5 cm be carried by a truck whose capacity to carry load is 6 metric tons ? One cubic meter of bricks weighs 2000 kg. [1 metric ton = 1000 kg]
6. A field is 200 m long and 75 m broad; and a tank 40 meter long, 20 meter broad and
10 meter deep is dug in the field, and the earth taken out of it is spread evenly over the
field. How much is the level of field raised ?
7. Four cubes each of sides 5 cm are joined end to end. Find the surface area of the resulting cuboid.
8. The sides of an open box are 0.5 cm thick and bottom is 1 cm thick. If the internal length, breadth and depth are respectively 14 cm, 10 cm ad 8 cm, find the quantity of material used in the construction of the box.
9. Find the whole surface area of a hollow cylinder open at the ends, if its length is 10 cm, the internal diameter is 8 cm and the thickness is 1 cm [Use π = 3.14]
10. A cubic cm of gold is drawn into a wire 1/5 mm in diameter; find the length of wire. ( π = 3.14)
11. A well with 8.4 meter inside diameter is dug 10 meter deep. Earth taken out of it has been spread all around it to a width of 4 meters to form an embankment. Find the height of the embankment.
12. Find the slant height of a cone whose volume is equal to 12936 cubic meters and the diameter of whose base is 42 meters.
13. The volume of a cone is 616 cubic meters. If the height of cone is 27 meters, find the radius of its base.
14. A conical vessel of internal radius 14 cm and height 36 cm is full of water. If this water is poured into a cylinder with internal radius 21 cm, find the height to which the water rises in the cylinder.
15. Find the diameter of a sphere whose volume is 606.375 cubic meter.
16. A room 12 meters long, 4 meters broad and 3 meters high has two windows 2 m × 1 m and a door 2.5 m × 2 m. Find the cost of papering the walls with paper 50 cm wide at Rs 20 per meter.
17. A hall, whose length is 15 m and breadth is twice its height, takes 250 meters of paper 2 meters wide for its four walls. Find the area of the floor.
18. The length of a room is 1.5 times its breadth. The cost of carpeting it at Rs 150 per square meter is Rs 14400 and the cost of white washing the four walls at Rs 5 per square meter is Rs 625. Find the dimensions of the room.
IX Maths Surface Areas and Volumes Concepts Chapter 13
2. Find the number of 5 cm cubes that can be cut out of a 15 cm cube. 3. Three cubes of metals whose edges are 3, 4 and 5 cm respectively are melted and formed into a single cube. If there is no waste in the process, find the edge of the new cube so formed.
4. A school room is to be built to accommodate 70 children, so as to allow 2.2 sq m of floor area and 11 cu m of space for each child. If the room is to be 14 m long, what must be its breadth and height ?
5. How many bricks 20 cm × 10 cm × 7.5 cm be carried by a truck whose capacity to carry load is 6 metric tons ? One cubic meter of bricks weighs 2000 kg. [1 metric ton = 1000 kg]
6. A field is 200 m long and 75 m broad; and a tank 40 meter long, 20 meter broad and
10 meter deep is dug in the field, and the earth taken out of it is spread evenly over the
field. How much is the level of field raised ?
7. Four cubes each of sides 5 cm are joined end to end. Find the surface area of the resulting cuboid.
8. The sides of an open box are 0.5 cm thick and bottom is 1 cm thick. If the internal length, breadth and depth are respectively 14 cm, 10 cm ad 8 cm, find the quantity of material used in the construction of the box.
9. Find the whole surface area of a hollow cylinder open at the ends, if its length is 10 cm, the internal diameter is 8 cm and the thickness is 1 cm [Use π = 3.14]
10. A cubic cm of gold is drawn into a wire 1/5 mm in diameter; find the length of wire. ( π = 3.14)
11. A well with 8.4 meter inside diameter is dug 10 meter deep. Earth taken out of it has been spread all around it to a width of 4 meters to form an embankment. Find the height of the embankment.
12. Find the slant height of a cone whose volume is equal to 12936 cubic meters and the diameter of whose base is 42 meters.
13. The volume of a cone is 616 cubic meters. If the height of cone is 27 meters, find the radius of its base.
14. A conical vessel of internal radius 14 cm and height 36 cm is full of water. If this water is poured into a cylinder with internal radius 21 cm, find the height to which the water rises in the cylinder.
15. Find the diameter of a sphere whose volume is 606.375 cubic meter.
16. A room 12 meters long, 4 meters broad and 3 meters high has two windows 2 m × 1 m and a door 2.5 m × 2 m. Find the cost of papering the walls with paper 50 cm wide at Rs 20 per meter.
17. A hall, whose length is 15 m and breadth is twice its height, takes 250 meters of paper 2 meters wide for its four walls. Find the area of the floor.
18. The length of a room is 1.5 times its breadth. The cost of carpeting it at Rs 150 per square meter is Rs 14400 and the cost of white washing the four walls at Rs 5 per square meter is Rs 625. Find the dimensions of the room.
IX Maths Surface Areas and Volumes Concepts Chapter 13
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