Holidays Home Work

Mathematics – Class X

1. The diameters of front and rear wheel of a tractor are 80 cm and 2 m respectively. Find the number of complete revolutions that the rear wheel will make to cover the same distance as covered by front wheel in 800 revolutions
   
2. A square is inscribed in a circle of radius 'r'. Find the ratio of their areas
   
3. Four circles each of radius 6 cm touch each other externally. Find the area enclosed between the circles
   
4. The area of equilateral triangle is 49√3 cm². Taking each angular point as centre a circle is described with radius half the length of the side of the triangle. Find the area of triangle not included in the circles.
   
5. It is proposed to add two circular ends to a square lawn on the adjacent sides which measures 50 m on each side. The centre of the circular ends being the point of intersection of diagonals of the square. Find the area of the whole lawn
   
6. A circular park is surrounded by a path of width 0.7 m. If the radius of the park is 41.3 m, find the cost of paving the path at the rate of Rs. 200 per m²
   
7. If the perimeter of a sector of a circle of radius 7 cm is 16.2 cm, find the central angle of the sector
   
8. A wire of length 18 cm is bent to form a sector of a circle of radius 4 cm. Find the area of sector so formed
   
9. If three circles of radius 'a' each, are drawn such that each touches the other two, prove that the area between them is 4a²/25
   
10. Three horses are tethered with 7 m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also find the area of the field which remains ungrazed
    
11. A golf ball has diameter of 4.1 cm. Its surface has 150 hemispherical dimples each of radius 2 mm. Calculate the total surface are of the ball which is exposed to the surroundings
    
12. A rectangular sheet of tin 44 cm x 20 cm is rolled along its length to form a cylinder. Find the volume and its surface area. Find the difference in surface area and volume if it is rolled along its breadth
    
13. A solid cylinder has a total surface area of 231 cm². Its lateral surface area is 2/3^rd of the total surface area. Find the volume of the cylinder
    
14. Water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 7 m/s in to a cylindrical tank whose base radius is 40 cm. By how much will the level rise in 1 hour
    
15. The barrel of a fountain pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used upon writing 990 words on an average. How many words would use up a bottle of ink containing one fourth of a litre
    
16. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27^th of the volume of the given cone, at what height above the surface of the base is the section made
    
17. A semicircular sheet of metal of diameter 28 cm is bent to form a conical cup. Find the capacity of the cup
    
18. The total surface area of a cube is numerically equal to the surface area of a sphere. Show that the ratio of their volumes is √π : √6
    
19. Water flows at the rate of 20 m/s from a cylindrical pipe 5 mm in diameter. Find the time it would take to fill a conical vessel whose diameter of the base is 40 cm depth 24 cm
    
20. The height of a circular cylinder is 6 m. Three times the sum of areas of its two circular faces is twice the area of its curved surface. Find the radius of the base
    

    
     

    Assignments for Chapter 2, 7 & 15 will be uploaded soon