Assignment - Surface Area and Volumes, Class 9 Mathematics PDF Download

VERY SHORT ANSWER TYPE QUESTIONS :

1. Write the lateral surface area of a cuboid having length ℓ units, breadth b units and height h. units.

2. Write the total surface area of a cuboid having three edges of length as 10 cm, 5 cm and 3 cm.

3. Write the curved surface area of a right circular cylinder whose radius is 3 cm and height is 5 cm.

4. The volume of a right cylinder having base radius 10 cm is 600 π cm³. Find the height of the cylinder.

5. Write the curved surface area of a right circular cone having radius 7 cm and slant height 10 cm. (Take π = 22/7)

6. Write the total surface area of a right circular solid cone having radius 10 cm and slant height 25 cm. (Take π = 22/7)

7. Find the vertical height of a right circular cone whose radius is 6 cm and slant height is 10 cm.

8. Find the volume of a right circular cylinder having radius 8 cm and height 10·5 cm. (Take π = 22/7)

 9. Write the volume of a right circular cone having radius r and height h.

10. Find the quantity of water in litres in a hemispherical bowl of radius 21 cm. The bowl is completely filled with water.  (Take π = 22/7)

11. The volume of a cuboid is 440 cm³ and the area of its base is 88 cm². Find its height.

12. The volume of a cube is 1000 cm. Find its total surface area.

13. How many 3 metre cubes can be cut from a cuboid measuring 18 m × 12 m × 9 m?

SHORT ANSWER TYPE QUESTIONS : QUESTIONS BASED ON CUBOID & CUBE

1. The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 m2. Find the dimensions.

2. Three cubes each of side 5 m are joined end to end. Find the surface area of the resulting cuboid.

3. A swimming pool is 20 m in length, 15 m in breadth, and 4 m in depth. Find the cost of cementing its floor and walls at the rate of Rs. 12 per square metre.

4. A cuboid has total surface area of 40 m² and its lateral surface area is 26 m². Find the area of its base.

5. The length of a cold storage is double its breadth. Its height is 3 metres. The area of its four walls (including doors) is 108 m². Find its volume.

6. The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

7. An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface at Rs. 50 per sq. metre.

8. A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm. Find the rise in water level in the vessel.

9. A solidcube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboids.

10. Three metal cubes whose edges measure 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find its edge. Also, find the surface area of the new cube.

QUESTIONS BASED ON RIGHT CIRCULAR CYLINDER

11. The area of the base of a right circular cylinder is 154 cm² and its height is 15 cm. Find the volume of the cylinder.

12. The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder, assuming it is open at either end.

13. The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm³. Find its radius. (Use π = 22/7)

14. The volume of metallic cylindrical pipe is 748 cm³. Its length is 14 cm and its external radius is 9 cm. Find its thickness.

QUESTIONS BASED ON RIGHT CIRCULAR CONE

15. The diameter of a cone is 14 cm and its slant height is 9 cm. Find the area of its curved surface.

16. Find the total surface area of a cone, if its slant height is 9 m and the radius of its base is 12 m.

17. The radius of a cone is 3 cm and vertical height is 4 cm. Find the area of the curved surface.

18. The radius and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm², find its radius. (Use π = 22/7)

19. The lateral surface of a cylinder is equal to the curved surface of a cone. If the radius be the same, find the ratio of the height of the cylinder and slant height of the cone.

20. Find the volume of a right circular cone 1.02 m high, if the radius of its base is 28 cm.

21. The diameter of a right circular cone is 8 cm and its volume is 48 πcm³. What is its height?

22. A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

23. A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises.

24. A cone and a cylinder are having the same base. Find the ratio of their heights if their volumes are equal.

QUESTIONS BASED ON SPHERE

25. Find the surface area and total surface area of a hemisphere of radius 21 cm.

26. A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved surface.

27. Show that the surface area of a sphere is the same as that of the lateral surface of a right circular cylinder that just encloses the sphere.

28. The internal and external diameters of a hollow hemi-spherical vessel are 24 cm and 25 cm respectively. The cost of paint one sq. cm of the surface is 7 paise. Find the total cost to paint the vessel all over. (ignore the area of edge).

29. Find the volume of a sphere whose surface area is 154 square cm.

30. A solid sphere of radius 3 cm is melted and then cast into small spherical balls each of diameter 0.6 cm. Find the number of balls thus obtained.

31. How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter.

32. A solid lead ball of radius 7 cm was melted and then drawn into a wire of diameter 0.2 cm. Find the length of the wire.

LONG ANSWER TYPE QUESTIONS :

1. Length of a class-room is two times its height and breadth is  times its height. The cost of white-washing the walls at the rate of Rs. 1.60 per m² is Rs. 179.20. Find the cost of tiling the floor at the rate of Rs. 6.75 per m².

2. The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rate of Rs. 4 and Rs. 4.50 per square metre is Rs. 416. Find the dimensions of the box.

3. Find the number of bricks, each measuring 25 cm × 12.5 cm × 7.5 cm required to construct a wall 6 m long, 5 m high and 0.5 m thick, while the cement and sand mixture occupies 1/20 of the volume of the wall.

4. A class room is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m × 1.4 m and three windows, each measuring 2 m × 1m. The interior walls are to be colour washed. The contractor charges Rs. 5.25 per sq. m. Find the cost of colour washing.

5. A room is half as long again as it is broad. The cost of carpeting the room at Rs. 3.25 per m² is Rs. 175.50 and the cost of papering the walls at Rs. 1.40 per m² is Rs. 240.80. If 1 door and 2 windows occupy 8 m², find the dimensions of the room.

6. A wooden bookshelf has external dimensions as follows : Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm 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.

7. In fig. the shape of a solid csopper piece (made of two pieces with dimensions as shown in the figure) is shown. The face ABCDEFA is the uniform cross section. Assume that the angle at A,B,C,D,E and F are right angles. Calculate the volume of the piece.

8. A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10 m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. Find the depth of the drainlet.

9. A metallic sheet is of the rectangular shape with dimensions 48 cm × 36 cm. From each one of its corners, a square of 8 cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box. 10. Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate in 30 min, if 9 cm of standing water is desired?

QUESTIONS BASED ON RIGHT CIRCULAR CYLINDER

11. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 c.c. of iron weighs 8 gm.

12. A solid cylinder has total surface area of 462 square cm. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder. (Take π = 22/7)

13. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width
of 5 m to form an embankment. Find the height of embankment.

QUESTIONS BASED ON RIGHT CIRCULAR CONE

14. A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs. 2 per square metre, if the radius of the base is 14 metres.

15. A solid cube of side 7 cm is melted to make a cone of height 5 cm, find the radius of the base of the cone.

16. From a right circular cylinder with height 10 cm and radius of base 6 cm, a right circular cone of the same
height and base is removed. Find the volume of the remaining solid.

QUESTIONS BASED ON SPHERE

17. The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm² surface is Rs. 0.05. Find the total cost to paint the vessel all over. (Use π= 22/7)

18. A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone
is 6 cm and its height is 4 cm. Find the cost of painting the toy at the rate of Rs. 5 per 1000 cm².

19. The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in fig. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint costs 5 paise per cm².

20. A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone.

ANSWER KEY

VERY SHORT ANSWER TYPE QUESTIONS :

1. 2 (ℓ + b)h
2. 190 cm²
3. 30 πcm²   
4. 6 cm
5. 220 cm²
6. 1100 cm²
7. 8 cm                          
8. 2112 cm³
9. 13 πr²h                      
10. 19.404 litres
11. 5 cm                        
12. 600 cm²
13. 72

SHORT ANSWER TYPE QUESTIONS :

1. 2 m, 4 m and 6 m              
2. 350 cm²
3. Rs. 6960                          
4. 7 m²
5. 216 m³                             
6. 240 cm²
7. Rs. 279.70                        
8. 4.05 cm
9. 3 : 2                                
10. 6 cm, 216 cm²
11. 2310 cm³                       
12. 5720 cm³
13. 5 cm                              
14. 1 cm
15. 198 cm²                                  
16. 792 m²
17. 62.85 cm²                       
18. 12 cm
19. 1 : 2                                  
20. 83776 cm³
21. 9 cm                                
22. 6.4 cm
23. 2 cm                                 
24. 3 : 1
25. 2772 cm² ; 4158 cm²        
26. 4 : 4 : 5
28. Rs. 132.11                        
29. 179.66 cm³
30. 1000                                
31. 2541    
32. 457.33 m

LONG ANSWER TYPE QUESTIONS :

1. Rs. 324                    
2. 8 m, 12 m and 16 m                  
3. 6080
4. Rs. 513.45
5. length = 9m, breadth = 6m and height = 6 m              
6. Rs. 6275
7. 880 cm³                   
8. 1.227 m                                  
9. 5120 cm³
10. 4,00,000 m²           
11. 1424.304 kg                        
12. 539 cm³
13. 4.66 m                  
14. Rs. 2068
15. 8.09 cm                  
16. 754.28 cm³                       
17. Rs. 96.28
18. 51 paise                  
19. Rs. 382.80                          
20. 3 cm