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NCERT Exemplar · Class 10 Mathematics Surface Areas and Volumes

62 questions · 62 still being checked

EXERCISE 12.1 1–10 (part 1 of 7)

  1. Choose the correct answer from the given four options:

    Exercise 1

    A cylindrical pencil sharpened at one edge is the combination of
    (A)
    a cone and a cylinder
    (B)
    frustum of a cone and a cylinder
    (C)
    a hemisphere and a cylinder
    (D)
    two cylinders.

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    (A)
    (A) a cone and a cylinderA sharpened pencil's tip is conical while its shaft is a cylinder.

  2. Exercise 2

    A surahi is the combination of
    (A)
    a sphere and a cylinder
    (B)
    a hemisphere and a cylinder
    (C)
    two hemispheres
    (D)
    a cylinder and a cone.

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    (A)
    (A) a sphere and a cylinderA surahi's round body is a sphere and its narrow neck is a cylinder.

  3. Exercise 3

    A plumbline (sahul) is the combination of (see Fig. 12.2\displaystyle 12.2)
    (A)
    a cone and a cylinder
    (B)
    a hemisphere and a cone
    (C)
    frustum of a cone and a cylinder
    (D)
    sphere and cylinder
    NCERT_Question_Class10_Maths_Exemplar_Ch12_Ex12-1_Q3

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    (B)
    (B) a hemisphere and a coneThe rounded top of the plumbline is a hemisphere and the tapering lower part ending in a point is a cone.

  4. Exercise 4

    The shape of a glass (tumbler) (see Fig. 12.3\displaystyle 12.3) is usually in the form of
    (A)
    a cone
    (B)
    frustum of a cone
    (C)
    a cylinder
    (D)
    a sphere
    NCERT_Question_Class10_Maths_Exemplar_Ch12_Ex12-1_Q4

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    (B)
    (B) frustum of a coneThe glass is wider at the open rim than at the base, with straight slanted sides -- the shape of a cone with its narrow top cut off.

  5. Exercise 5

    The shape of a gilli, in the gilli-danda game (see Fig. 12.4\displaystyle 12.4), is a combination of
    (A)
    two cylinders
    (B)
    a cone and a cylinder
    (C)
    two cones and a cylinder
    (D)
    two cylinders and a cone
    NCERT_Question_Class10_Maths_Exemplar_Ch12_Ex12-1_Q5

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    (C)
    (C) two cones and a cylinderThe gilli has a cylindrical middle section with a cone tapering to a point at each end.

  6. Exercise 6

    A shuttle cock used for playing badminton has the shape of the combination of
    (A)
    a cylinder and a sphere
    (B)
    a cylinder and a hemisphere
    (C)
    a sphere and a cone
    (D)
    frustum of a cone and a hemisphere

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    NCERT’s answer
    (D)
    (D) frustum of a cone and a hemisphereThe cork base is a hemisphere and the feather skirt flares outward like a frustum of a cone.

  7. Exercise 7

    A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
    (A)
    a frustum of a cone
    (B)
    cone
    (C)
    cylinder
    (D)
    sphere

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    NCERT’s answer
    (A)
    (A) a frustum of a coneThe leftover solid between the base circle and the cut, once the smaller cone above the plane is removed, is a frustum.

  8. Exercise 8

    A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5\displaystyle 0.5 cm and it is assumed that 18\displaystyle \frac{1}{8} space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is
    (A)
    142296\displaystyle 142296
    (B)
    142396\displaystyle 142396
    (C)
    142496\displaystyle 142496
    (D)
    142596\displaystyle 142596

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    (A)
    (A) \(\displaystyle 142296\)One-eighth of the cube stays unfilled, so marbles occupy \(\displaystyle \tfrac{7}{8}\) of its volume.\[V_{\text{cube}} = 22^3 = 10648 \text{ cm}^3 \] \[V_{\text{filled}} = \frac{7}{8}\times 10648 = 9317 \text{ cm}^3 \] \[V_{\text{marble}} = \frac{4}{3}\pi r^3 = \frac{4}{3}\cdot\frac{22}{7}\cdot(0.25)^3 = \frac{11}{168} \text{ cm}^3 \] \[n = 9317 \div \frac{11}{168} = 142296 \]

  9. Exercise 9

    A metallic spherical shell of internal and external diameters 4\displaystyle 4 cm and 8\displaystyle 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is
    (A)
    12cm
    (B)
    14cm
    (C)
    15cm
    (D)
    18cm

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    (B)
    (B) \(\displaystyle 14 \text{ cm}\)Melting conserves volume, so the shell's volume equals the cone's volume.\[V_{\text{shell}} = \frac{4}{3}\pi(R^3-r^3) = \frac{4}{3}\pi(4^3-2^3) = \frac{224\pi}{3} \text{ cm}^3 \] \[V_{\text{cone}} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi(4)^2 h = \frac{16\pi h}{3} \] \[\frac{224\pi}{3} = \frac{16\pi h}{3} \implies h = 14 \]

  10. Exercise 10

    A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is
    (A)
    21cm
    (B)
    23cm
    (C)
    25cm
    (D)
    19cm

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    (A)
    (A) \(\displaystyle 21 \text{ cm}\)Moulding conserves volume, so the cuboid's volume equals the sphere's volume.\[V_{\text{cuboid}} = 49\times33\times24 = 38808 \text{ cm}^3 \] \[\frac{4}{3}\pi r^3 = 38808 \] \[r^3 = 38808\times\frac{3}{4}\times\frac{7}{22} = 9261 \] \[r = \sqrt[3]{9261} = 21 \]