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Surface Area An...

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  • Question 1
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    Two cuboids, each of breadth 3 cm, length 6 cm and height 6 cm, are joined to form a cube. What is the total surface area of the resultant cube?

  • Question 2
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    If the volume of a cube is (12)3 m3, then the total surface area of the cube is equal to

  • Question 3
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    If the radius of a hemisphere is 3 cm, then its total surface area is

  • Question 4
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    The length and the breadth of a cuboidal box are 2 m and 0.5 m, respectively. If the lateral surface area of the box is 7.5 m2, its height is

  • Question 5
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    The height of a right circular cone, whose base radius is 5 cm and volume is 25 cm3, is

  • Question 6
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    If V, p and q are the volume, base radius and height of a right circular cylinder, respectively, then which of the following relationships is true?

  • Question 7
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    A hemisphere of diameter d is surmounted by a cone of radius (as shown in the figure) unit. If the height of the figure is twice the height of the hemisphere, which of the following expressions gives the volume of the figure?

  • Question 8
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    A cone of height 15 cm and diameter 7 cm is mounted on the base of a hemisphere of same radius. Find the volume of the combination so formed.

  • Question 9
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    A rectangular cuboid block of dimensions 18 cm x 12 cm x 9 cm is cut into an exact number of equal cubes. Find the possible number of cubes.

  • Question 10
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    A sphere of copper, whose diameter is 18 cm, is melted and converted into a wire of diameter 4 mm. The length of the wire (in metres) is

  • Question 11
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    A hollow iron pipe is 42 cm long and its inner radius is 7 cm. If the thickness of the pipe is 1.5 cm and iron weights 10 gm/cm3, find the mass of the pipe (in kg).

  • Question 12
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    Water is pumped out through a cylindrical pipe of internal diameter 28 cm. How much water is pumped out in one hour if the flow velocity of water is 4 cm/s?

  • Question 13
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    The water level in a cylindrical beaker, having a base radius 10 cm, is at a height of 14 cm from the base. If a metallic sphere of radius 3 cm is put into this beaker, what will be the rise in the water level?

  • Question 14
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    A tank 12 m long and 8 m wide contains water up to a height of 2.5 m. The total area of the wet surface is

  • Question 15
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    If the dimensions of a cuboid are increased by 15%, 10% and 5%, respectively. Find the approximate percentage increase in its volume.

  • Question 16
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    A wooden box measures externally 4 m x 3 m x 2 m. The thickness of all four sides is 5 cm. If the capacity of the box is 18.096 m3, find the thickness of the bottom.

  • Question 17
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    A cylinder is formed by folding a rectangular tin sheet along its length, and the dimensions of the sheet are 44 cm by 20 cm. What is the curved surface area of the cylinder?

  • Question 18
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    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 of the volume of the cone, the height at which the section is made is

  • Question 19
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    A sphere of diameter 6 cm is dropped into a right circular cylindrical vessel, partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, then by how much level will water rise in the cylindrical vessel?

  • Question 20
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    A circus tent is in the form of a cone over a cylinder. The diameter of the base is 6m, the height of cylindrical part is 15 m and the total height of the tent is 19 m. The canvas required for the tent is

  • Question 21
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    The external dimensions of an open box are 25 cm (length), 20 cm (breadth) and 12 cm (height). Its thickness is 2 cm. If 1 cm3 of metal used in the box weighs 0.5 gm, find the weight of empty box.

  • Question 22
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    A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. What is the area of the curved surface for the conical portion?

  • Question 23
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    Directions: Study the statements carefully:

    Statement I:     If the radius of a cone is increased by 50% and the height is decreased by 20%, then the volume increases by 80%.
    Statement II: If the length of a cuboid is increased by 25%, the width is decreased by 75% and the height is decreased by 20%, then the volume decreases by 75%.

    Which of the following options holds?

  • Question 24
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    The total cost of white-washing the four walls of a room is Rs. 6520. The length, width and height of the room are 20 m, 16 m and 25 m, respectively. Find the approximate values of the following:

    (a) Per m2cost of white-washingthe four walls
    (b) Total cost of white-washing, if the area of doors and windows which occupy the area of 34 m2is ignored

  • Question 25
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    Match the following:

    Column - I Column - II
    (P) The curved surface area of a right circular cone, whose base radius is 13 cm and slant height is 15 cm, is 1. 1734 cm2
    (Q) If the volume of a cube is 4913 cm3, then the total surface area of the cube is equal to 2. 252π cm2
    (R) The lateral surface area of a right circular cylinder with base radius 7 cm and height 20 cm is 3. 880 cm2
    (S) The volumes of two spheres are in the ratio 64 : 27. If the sum of their radii is 21 cm, the difference between their surface areas will be 4. 195π cm2

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