Assignment CBSE IX Mathematics Surface area and volume

Assignment Class-IX  Mathematics  Topic – Surface area and volume

1.The diameter of  garden cylindrical roller is 2.8m long . How much area will it cover in 100 revolutions.

2. A rectangular piece of paper 16 cm by 3.5cm is rotated about the longer side. Find the   total surface area of the solid so generated.

3. In a hot water heating system, there is a cylindrical pipe of length 35m and radius 4cm  find the total radiating surface in the system

4. Find the curved surface area of the right circular cone whose slant height is 10cm and    base radius is 7cm.

5. The lateral surface area of the right circular cone of radius 12cm is 489.84 cm² . Find the height of the cone .

6. Find the surface area  of the sphere of radius 7cm.

7. A solid cube of side 14cm is cut into 64 cubes of equal volume. What will be the side

    of the new cube . Also find the ratio between their surface area.

8. The capacity of a cuboidal water tank is 240000 liters . Find the depth of the water tank if its length and breadth are 5m and 3m respectively.

9.Find the capacity of a cold storage of breadth 4.5m, height 3m and length double its breadth

10. Slant height and depth of a conical pit are 35cm and 28cm respectively . Find the  volume of a conical pit.

11. The base radii of two right circular cones of same height are in the ratio 4:7. Find the  ratio of their volumes.

12.The dimensions of a cuboid are in the ratio 2:3:4 and its total surface area is 8788cm². Find the dimensions of the cuboid.

13. A closed cuboidal iron water tank is 12m long, 9m wide and 4m high is to be made from an iron sheet of breadth 2m . Find the cost of iron sheet at the rate of Rs 45 per   metre.

14. The diameter of a cylindrical road roller is 98cm and its length is 150cm. It takes 750  revolutions to move once over a road to level it . Find the cost of leveling the road at    the rate of Rs.2.50 per m²

15. The inner diameter of a cylindrical pit is 56cm and it is 240cm deep. Find : (i)   its inner curved surface area    (ii)  its total inner surface area (iii) the cost of plastering the inner surface area at the rate of Rs. 43 per square metre.

17. How many metres of cloth, 5m wide will be required to make a conical tent of base  radius 7m and height 24m ? Also find the cost of the cloth at the rate of Rs 45 per   metre.

18. A joker’s cap is in the form of a right circular cone of base radius 5cm and height  12cm. Find the area of the sheet required to make 15 such caps.

19. A right triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side 12cm  and 5cm respectively . Find the ratio of the total surface area of the two cones so formed.    

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

21.The radius of the spherical balloon increases from 10.5cm to 14cm as air is being  pumped into it. Find the ratio of surface area of the balloon in the two cases.

22. Water in a river , 3m wide and 1.2m deep, is flowing at the rate of 20km per hour . How much area will it irrigate in half an hour, if 10cm of  standing water is desired.

22. Find the mass of  metallic hollow cylindrical pipe 24cm long with internal diameter 10cm and made of 5mm thick metal, if 1cm³ of the metal weighs 7.5g.

23. A shot- put is a metal sphere of radius 4.9cm. If the density of the metal is 7.8g per  cm³. Find the mass of the shot –put.

24. A brass bowl is in the form of a hemisphere . The cost of tin plating it on the inside at the rate of  Rs 16 per 100 cm² is Rs 27.72. Find the :  (i)  inside surface area of the bowl  (ii) volume of the air inside the bowl  

CBSE X Mathematics Coordinate Geometry Extra scoring guess paper 2014

1) Show that the points (a, a), (-a, - a) and (- √3a, √3a) are the vertices of an equilateral Δ

2) Show that four points (0,-1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle

3) Prove that (4, -1), (6, 0), (7, 2) and (5, 1) are the vertices of a rhombus. Is it a square?

4) Show that the following points are the vertices of a right angled isosceles triangle: (1, 2), (1, 5) and (4, 2)

5) Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5) (x - y = 2)

6) If the distance of P(x, y) from the points A (3, 6) and B (-3, 4) are equal, prove that 3x + y = 5

7) Find the values of x for which the distance between the points P (2, -3) and Q (x, 5) is 10 units (8 or -4)

8) Given A (-2, 3) and AB = 10 units .If ordinate of B is 9, find abscissa of B (-10, 6)

9) Find the coordinates of the point equidistant from three given points A (5, 1), B (-3, -7) and C (7, -1) (2,-4)

10) If the point p(x, y) is equidistant from the points A (a + b, b - a) and B (a - b, a + b), prove that b x = a y

11) Find the point on y- axis which is equidistant from the point (5, -2) and (-3, 2) (0, -2)

12) Find the point on x- axis which is equidistant from the points (2, -5) and (-2, 9) (-7, 0)

13) If the points A (4, 3), and B(x, 5) are on the circle with the centre. O (2, 3), find the value of x (x=2)

14) The three consecutive vertices of a parallelogram are (-2, 1), (1, 0) and (4, 3). Find the Coordinates of the fourth vertex (1, 4)

15) Find the value of k for which the points (7, -2), (5, 1), and (3, k) are collinear. (k = 4)

16) Find the value of m, for which the points with co-ordinates (3, 5), (m, 6) and [1/2, 15/2] are collinear (m = 2)

17) Find a relation between x and y, if (x, y), (1, 3) and (8, 0) are collinear (3x +7y = 24)

18) If the points (-2, 1), (a, b) and (4,-1) are collinear and a - b = 1, then find the values of a and b (a =1, b = 0)

19) Check whether the points (4, 5), (7, 6) and (6, 3) are collinear.

20) If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

21) ABCDE is polygon whose vertices are A (-1, 0), B (4, 0), C (4, 4), D (0, 7) and E (-6, 2). Find the area of the polygon

22) Using A (4, -6), B (3, -2) and C (5, 2), verify that a median of the ΔABC divides it into two triangles of equal areas

23) The coordinates of A, B, C are (3, 4), (5, 2), (x, y) respectively. If area of ∆ABC = 3, show that x + y = 10

24) The coordinates of the vertices of ΔABC are A (4, 1), B (-3, 2) and C (0, k).Given that the area of ΔABC is 12 unit2, Find the Value of k (k = - 13/ 7)

25) Find the ratio in which the point (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7) (4: 1)

26) If P divides the join of A (-2, -2) and B (2, -4) such that AP/AB = 3/7, find the coordinates of P (-2/7, -20/7)

27) Find the ratio in which the line 2x + y – 5 = 0 divides the line segment joining A (2,-3) and B (3, 9) (2:5) 

28) Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 7) (k = - 6/25) 

29) Find the length of medians of triangle whose vertices are A (-1, 3), B (1, -1), and C (5, 1)

30) If the midpoint of of the segment joining A (a, b +1), and B (a +1, b +2) is C (3/2, 5/2) Find a and b (a=1, b=1)

31 The coordinates of one end point of a diameter of a circle are (4, -1) and the coordinates of the centre of the circle are (1, -3) Find the coordinates of the other end of the diameter (-2, -5)

32) If P(x, y) is any point on the line joining the points A (a, 0), B (0, b), then show that x/a + y/b = -1

33) The centre of a circle is (2a – 1, 7) and it passes through the point (-3, -1). If the diameter of the circle is 20 units, then find the value of a (-4, 2)

34) Determine the value of a if AB = BC, where A, B, C are the points (-5, 1), (0, 5) and (a, 1) respectively (±5)

35) A (5, -1), B (-1, 8) and C (-3, -2) are the vertices of triangle ABC. E and F are the midpoints of the sides AB and AC Respectively. Show that EF = ½ BC

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability

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