Chap-13 MCQs - AMU/JMI XI-Dip.Engg. Entrance Test

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Maths Class X Chap-1 , Chap-2 ,Chap-3 ,Chap-4 , Chap-5 ,Chap-6 ,Chap-7 ,Chap-8 ,Chap-9 ,Chap-10 ,Chap-11 ,Chap-12 ,Chap-13 ,Chap-14, Chap-15
Chapter 13 : Surface Areas and Volumes            Answers
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Chapter 13 Class IX

1a. Find the surface area of cuboid whose length is twice its width, width is twice its height and height is equal to 1cm.

a)      24 cm²

b)      28 cm²

c)      30 cm²

d)     32 cm²

2a. The surface area of cube whose side is 1m.

a)      1 m²

b)      4 m²

c)      6 m²

d)     8 m²

3a. Find the lateral surface area of cuboid whose length is twice its width, width is twice its height and height is equal to 1cm.

a)      12 cm²

b)      14 cm²

c)      16 cm²

d)     18 cm²

4a.The inside of a hall is 4m wide and 6 long, the clear height of the hall is 3m.The hall has two doors of dimension 1m x 2m.Find cost of painting of interior of hall walls if it cost Rs.100 per square meter.

a)      Rs. 4600

b)      Rs. 5600

c)      Rs. 8000

d)     Rs. 8600

5a.The inside of a hall is 4m wide and 6 long, the clear height of the hall is 3m.The hall has two doors of dimension 1m x 2m.Find cost of painting of interior of hall walls and the ceiling of the hall, If it cost Rs.100 per square meter.

a)      Rs. 4600

b)      Rs. 5600

c)      Rs. 8000

d)     Rs. 8600

6a. Find the cost of square tiles of side10cm required to cover internal walls of a cubical tank of 3m side, if the cost of one tile is Rs.10.

a)      Rs.24000

b)      Rs.34000

c)      Rs.36000

d)     Rs.42000

7a. Find the cost of square tiles of side10cm required to cover internal walls and base of a tank of height, width and length as 3m, 4m and 6 respectively, if the cost of one tile is Rs.10.

a)      Rs.64000

b)      Rs.84000

c)      Rs.96000

d)     Rs.98000

8a. Find the area of sheet required to make a box open at the top, 2 m long, 1.5 m wide and 50 cm deep. Ignore the thickness of the sheet.

a)      5.5 sq.m

b)      6.5 sq.m

c)      7.5 sq.m

d)     65.5 sq.m

9a. If the perimeter of the floor of a rectangular hall of 3m height is 200, find the lateral surface area of rectangular hall.

a)      200 sq.m

b)      400 sq.m

c)      600 sq.m

d)     800 sq.m

10a. The numerical values of lateral surface area and the perimeter of base of cuboid is same if the height of the cuboid is

a)      1 unit

b)      2 units

c)       units

d)      units

11a. All the outer edges of a cuboidal box of length 50cm, width 20cm and height 15cm has to be covered with a tape. Find the length of the tape.

a)      280 cm

b)      320 cm

c)      340 cm

d)     580 cm

12a. The perimeter of the base of a cylinder is 100 cm. Find the curved surface area of the cylinder if its height is 15cm.

a)      1000 cm²

b)      1200 cm²

c)      1500 cm²

d)     3000 cm²

13a. If the circumference of the base of a cylinder is 50 cm. Find the total surface area of the cylinder is the sum of its height and base is 20.

a)      30 sq.m

b)      70 sq.m

c)      80 sq.m

d)     100 sq.m

14. Find the cost of paint required on the cylindrical walls 3 m high and the base radius 7m of a cylindrical tank open from the top. Given that cost of painting per sq.m is Rs.125.

a)      Rs. 15600

b)      Rs. 16000

c)      Rs. 16300

d)     Rs. 16500

15a. Find the area of sheet required to make a closed cylinder of 1.15 m high and base diameter 70 cm.

a)      2.3

b)      3.3

c)      5.7

d)     6.7

16a.  Find the total surface area of pipe of length h whose inner and outer radii are r and R respectively.

a)      π(r + R)(2h + R – r)

b)      π(r + R)(2h + R + r)

c)      π(r + R)( h + R + r)

d)     π(r + R)( h + R - 2r)

17a. Find the area of sheet required to make a cylinder open at one side of dia 140cm and height 10cm, if 5% of the steel actually used was wasted in making the tank.

a)      13300 cm²

b)      14400 cm²

c)      16600 cm²

d)     19800 cm²

18a. The curved surface area of a right circular cone of diameter d and height h is

        a) 4dπ√(d^2-4h^2 )

       b) 1/2 dπ√(d^2-4h^2 )

       c) 1/4 dπ√(d^2-4h^2 )

       d) 1/4 dπ√(d^2-4h^2 )

19a. The total surface area of a solid right circular cone of radius r and height h is

       a) πr(√(r^2+h^2 ) + r)

        b) πr(√(r^2+h^2 ))

       c) πr(r+h))

       d) π(r^2+h^2))

20a. Find the curved surface area of a cone whose diameter is 6cm and height is 4cm.

a)      47.14 cm²

b)      57.14 cm²

c)      100.25 cm²

d)     120.25 cm²

21a. Joining all points in space equidistant from a fixed point will give

a)      Circle

b)      Sphere

c)      Parabola

d)     Ellipse

22a. The total surface area of a solid hemisphere of diameter d is given by

a)     2πd²

b)    3πd²

c)     πd²

d)    πd²

23a. The ratio of curved surface area of a solid hemisphere to its surface area of flat circular portion is

a)      2:1

b)      1:2

c)      2:3

d)     3:2

24. The ration of diameters of two spheres is 1:3; find the ratio of their surface areas.

a)      1:2

b)      1:4

c)      1:3

d)     1:9

25a. A cubical box of side 14cm just encloses a sphere. Find the ratio of surface area of the sphere and the box. (Assume π = 22/7 )

a)      22:7

b)      7:22

c)      11:21

d)     21:11
Chapter 13 Class X

1. Find the total surface area of top whose shape is like a cone surmounted by a hemisphere as shown in fig. below. 

a)    77/2(3+√5)

b)    77/2(2+√5)

c)    77/2(1+2√5)

d)    77/2(1+3√5)

2. Wooden toy has hemisphere surmounted on a cylinder. Find the total surface area of the toy if height of the toy is 49cm and diameter of cylindrical portion is 14cm.

a)      2156

b)      2256

c)      4250

d)      5250

3. Find the total surface area of wooden piece whose length is a and diameter of its cylindrical portion is b as shown in fig below

a)    πb(2+a - b)

b)    πb(1+b - a)

c)    πb(b - a)

d)    πb(b + a)

4. A metallic toy is in the shape of a cone surmounted on a cylinder. Let the diameter of the cone and the cylinder be “d”, the slant height and the height of the cone and the cylinder be “l” and “2d” respectively. Find the total surface area of the toy.

a)    πd/8(l+9)

b)   πd/8(l - 9)

     c)    πd/4(2l+9d)

     d)    πd/4(2l - 9d)

5. 4 cubes each of volume 27cm³ are joined to form a big cube. Find the surface area of the resulting cube.

a)      32sq.cm

b)      34sq.cm

c)      76sq.cm

d)     96sq.cm

6. What is the surface area of the biggest sphere that can be made from a wooden cube of volume 343cm³?

a)      154 sq.cm

b)      174 sq.cm

c)      416 sq.cm

d)      616 sq.cm

7. The dimension of an ice cream block is 21cm x 14cm x 7cm. How much number of spoons of ice cream can be taken out from the ice cream block if the spoon is in the shape of hemisphere of 3.5cm diameter?

a)      20 approximately

b)      23 approximately

c)      26 approximately

d)     30 approximately

8. The 50cu.cm medicine powder has to be filled in capsules in shape of cylinder with hemispherical ends. If the total length of the capsule is 14 mm and the diameter of the capsule is 3.5 mm. find the number of capsules that can be filled by the medicine.

a)      97

b)      970

c)      257

d)     2570

9. Find the cost of a canvas tent in the shape of a cylinder surmounted by a cone. The slant height of the tent is 5.0m, both the diameter and height of cylindrical portion is 8m.The cost of tent per square metre is Rs. 1000.

a)      Rs.164000

b)      Rs. 264000

c)      Rs. 364000

d)     Rs. 464000

10. Find the volume of top whose shape is like a cone surmounted by a hemisphere as shown in fig. below. 

a)      179.7 cu.cm

b)      259.5 cu.cm

c)      359.5 cu.cm

d)     469.5 cu.cm

11. Find the volume of top whose shape is like a cone surmounted by a hemisphere as shown in fig. below. 

a)    (πd^3)/3

b)    (πd^3)/4

c)    (πd^3)/5

d)    (πd^3)/6

12. Find the volume of wooden piece whose length is a and diameter of its cylindrical portion is b as shown in fig below

a)   (πb^2)/12 (a-2b)

b)   (πb^2)/12 (a+ 2b)

c)   (πb^2)/12 (3a-b)

d)   (πb^2)/12 (3a+b)

13. If a metallic cone is melted to form a sphere, then

a)      The volume of sphere formed will be more than the volume of cone

b)      The volume of sphere formed will be less than the volume of cone

c)      The volume of sphere formed will be equal to the volume of cone

d)     The volume of sphere formed will be twice the volume of cone

14. A metallic toy is in the shape of a cone surmounted on a cylinder. Let the diameter of the cone and the cylinder be “d”, the height of the cone and the cylinder be “3d” and “d” respectively. Find the volume of the toy.

     a)   (πd^3)/4

     b)   (πd^3)/3

     c)   (πd^3)/2

     d)   πd^3

15. 4 cubes each of volume 27cm³ are joined to form a big cube. Find the volume of the resulting cube.

a)      108cu.cm

b)      128cu.cm

c)      216cu.cm

d)      512cu.cm

16. What is the volume of the biggest sphere that can be made from a wooden cube of volume 343cm³?

a)      159.9 cm³

b)      179.7 cm³

c)      189.5 cm³

d)      200.1 cm³

17. If a 10 cu.cm metallic cube of is melted to form a sphere, then surface area of sphere would be

a)      5 cu.cm

b)      7.5 cu.cm

c)      10 cu cm

d)     12.5 cu.cm

18. A metallic cone of base diameter 14cm and height 3.5cm is melted to from a sphere. Find the radius of sphere so formed.

a)      3.5 cm

b)      7.0 cm

c)      10.5 cm

d)     12.5 cm

19. Find the increase in water level is 1000 liters of water is poured in a tank of inner diameter 1.4m.

a)      50 cm

b)      65 cm

c)      75 cm

d)     100 cm

20. Find the decrease in water level if 770 liters water is used from an overhead tank of inner diameter 70cm.

a)      0.1 cm

b)      0.2 cm

c)      10 cm

d)      20 cm

21. A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of diameter 2mm. find the length of the wire.

a)      20 cm

b)      20 m

c)      40 cm

d)     40 m

21. A pump can fill a tank with rate of flow of 3.5lteres per second. Find the time take to fill a cylindrical tank of dia 70cm and height 70cm.

a)      1 min 47 sec

b)      1 min 37 sec

c)      1 min 27 sec

d)      1 min 17 sec

22. The ratio of volumes of a cylinder of x height & x diameter and a sphere of x diameter?

a)      2:3

b)      3:2

c)      3:4

d)     4:3

23. How many cones can be formed by meting a cylinder, if the height and the diameter of the come are same?

a)      2

b)      3

c)      4

d)      6

24. Volume of a frustum of a cone of height h, diameters D and d is

     a) 1/3 πh(D^2+d^2+Dd)

     b) 1/6 πh(D^2+d^2+Dd)

     c) 1/12 πh(D^2+d^2+Dd)

     d) 1/21 πh(D^2+d^2+Dd)

25. Curved surface area of a frustum of a cone of height h, larger diameter D and smaller diameter d is

      a) π/12(d+D)√(〖4h〗^2+(d+D)^2 )

      b) π/12(d+D)√(〖4h〗^2+(d+D)^2 )

      c) π/4(d+D)√(h^2+(d+D)^2 )

      d) π/4(d+D)√(〖4h〗^2+(d+D)^2 )

  Answers

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