Mensuration Model Question Paper

10th Standard EM

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Maths

Time : 02:00:00 Hrs
Total Marks : 60
    5 x 1 = 5
  1. If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

    (a)

    1:2

    (b)

    1:4

    (c)

    1:6

    (d)

    1:8

  2. If the radius of the base of a cone is tripled and the height is doubled then the volume is

    (a)

    made 6 times

    (b)

    made 18 times

    (c)

    made 12 times

    (d)

    unchanged

  3. A shuttle cock used for playing badminton has the shape of the combination of

    (a)

    a cylinder and a sphere

    (b)

    a hemisphere and a cone

    (c)

    a sphere and a cone

    (d)

    frustum of a cone and a hemisphere

  4. The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

    (a)

    \(\frac{4}{3}\pi\)

    (b)

    \(\frac{10}{3}\pi\)

    (c)

    \(5\pi\)

    (d)

    \(\frac{20}{3}\pi\)

  5. The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

    (a)

    1:2:3

    (b)

    2:1:3

    (c)

    1:3:2

    (d)

    3:1:2

  6. 8 x 2 = 16
  7. A cylindrical drum has a height of 20 cm and base radius of 14 cm. Find its curved surface area and the total surface area.

  8. A garden roller whose length is 3 m long and whose diameter is 2.8 m is rolled to level a garden. How much area will it cover in 8 revolutions?

  9. If one litre of paint covers 10 m2, how many litres of paint is required to paint the internal and external surface areas of a cylindrical tunnel whose thickness is 2 m, internal radius is 6 m and height is 25 m.

  10. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out (Fig.7.13). Find the total surface area of the remaining solid.

  11. Find the diameter of a sphere whose surface area is 154 m2.

  12. The internal and external radii of a hollow hemispherical shell are 3 m and 5 m respectively. Find the T.S.A. and C.S.A. of the shell.

  13. The slant height of a frustum of a cone is 5 cm and the radii of its ends are 4 cm and 1 cm. Find its curved surface area.

  14. A funnel consists of a frustum of a cone attached to a cylindrical portion 12 cm long attached at the bottom. If the total height be 20 cm, diameter of the cylindrical portion be 12 cm and the diameter of the top of the funnel be 24 cm. Find the outer surface area of the funnel.

  15. 3 x 5 = 15
  16. The volume of a cylindrical water tank is 1.078×106 litres. If the diameter of the tank is 7m, find its height.

  17. The ratio of the volumes of two cones is 2:3. Find the ratio of their radii if the height of second cone is double the height of the first.

  18. A metallic sphere of radius 16 cm is melted and recast into small spheres each of radius 2 cm. How many small spheres can be obtained?

  19. 3 x 8 = 24
  20. A solid iron cylinder has total surface area of 1848 sq.m. Its curved surface area is five – sixth of its total surface area. Find the radius and height of the iron cylinder.

  21. Th e radius of a sphere increases by 25%. Find the percentage increase in its surface area.

  22. A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm.

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