Chapter 12 · Surface Areas and Volumes

NCERT Exemplar Class 10 Maths Exercise 12.1

All 20 questions of NCERT Exemplar Class 10 Maths Exercise 12.1 (Surface Areas and Volumes), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   A cylindrical ​pencil ​sharpened ​at ​one ​edge ​is the combination of

   1. (a)a cone and a cylinder
   2. (b)frustum of a cone and a cylinder
   3. (c)a hemisphere and a cylinder
   4. (d)two cylinders.
   Show answer

   (a) a cone and a cylinder

   Step-by-step solution →
2. Q2
   A surahi is the combination of

   1. (a)a sphere and a cylinder
   2. (b)a hemisphere and a cylinder
   3. (c)two hemispheres
   4. (d)a cylinder and a cone
   Show answer

   (a) a sphere and a cylinder

   Step-by-step solution →
3. Q3
   A ​plumbline ​(sahul) ​is ​the ​combination of ​(see ​Fig. 12.2)

   1. (a)a cone and a cylinder
   2. (b)a hemisphere and a cone
   3. (c)frustum of a cone and a cylinder
   4. (d)sphere and cylinder
   Show answer

   (b) a hemisphere and a cone

   Step-by-step solution →
4. Q4
   The ​shape of ​a ​glass ​(tumbler) (see Fig. ​12.3) is usually in ​the form ​of

   1. (a)a cone
   2. (b)frustum of a cone
   3. (c)a cylinder
   4. (d)a sphere
   Show answer

   (b) frustum of a cone

   Step-by-step solution →
5. Q5
   The shape ​of a $gilli$, ​in the $gilli\text{-}danda$ game ​(see ​Fig. ​12.4), is ​a combination of

   1. (a)two cylinders
   2. (b)a cone and a cylinder
   3. (c)two cones and a cylinder
   4. (d)two cylinders and a cone
   Show answer

   (c) two cones and a cylinder

   Step-by-step solution →
6. Q6
   A ​shuttle ​cock used ​for ​playing badminton has the shape ​of ​the ​combination of

   1. (a)a cylinder and a sphere
   2. (b)a cylinder and a hemisphere
   3. (c)a sphere and a cone
   4. (d)frustum of a cone and a hemisphere
   Show answer

   (d) frustum of a cone and a hemisphere

   Step-by-step solution →
7. Q7
   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

   1. (a)a frustum of a cone
   2. (b)cone
   3. (c)cylinder
   4. (d)sphere
   Show answer

   (a) a frustum of a cone

   Step-by-step solution →
8. Q8
   A ​hollow cube ​of internal edge 22 cm is filled with spherical marbles of diameter 0.5 ​cm and it is assumed that $\frac{1}{8}$ ​space of ​the cube remains unfilled. Then the number of marbles that the cube can accommodate is

   1. (a)142296
   2. (b)142396
   3. (c)142496
   4. (d)142596
   Show answer

   (a) 142296

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9. Q9
   A metallic ​spherical shell of ​internal and ​external diameters $4\text{cm}$ and $8\text{cm}$, ​respectively is melted and recast into the form a cone of ​base ​diameter $8\text{cm}$. The height of ​the cone is

   1. (a)12 cm
   2. (b)14 cm
   3. (c)15 cm
   4. (d)18 cm
   Show answer

   (b) 14 cm

   Step-by-step solution →
10. Q10
    A solid ​piece of iron in the form of a cuboid of ​dimensions $49\text{cm}\times 33\text{cm}\times 24\text{cm}$ is ​moulded ​to form ​a solid ​sphere. The radius of the ​sphere is

    1. (a)21 cm
    2. (b)23 cm
    3. (c)25 cm
    4. (d)19 cm
    Show answer

    (a) 21 cm

    Step-by-step solution →
11. Q11
    A ​mason constructs a ​wall of dimensions $270\text{cm}\times 300\text{cm}\times 350\text{cm}$ with ​the bricks each of size $22.5\text{cm}\times 11.25\text{cm}\times 8.75\text{cm}$ and it is assumed that $\frac{1}{8}$ space is covered by ​the ​mortar. Then the number of bricks used to construct the wall is

    1. (a)11100
    2. (b)11200
    3. (c)11000
    4. (d)11300
    Show answer

    (b) 11200

    Step-by-step solution →
12. Q12
    Twelve solid ​spheres of the ​same size ​are made by ​melting ​a solid metallic cylinder of base diameter $2\text{cm}$ and height $16\text{cm}$. The diameter of each sphere ​is

    1. (a)4 cm
    2. (b)3 cm
    3. (c)2 cm
    4. (d)6 cm
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    (c) 2 cm

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13. Q13
    The radii ​of ​the top and bottom of a bucket ​of slant height ​45 cm ​are 28 cm and ​7 cm, respectively. The curved ​surface area of the bucket is

    1. (a)$4950$ cm${}^2$
    2. (b)$4951$ cm${}^2$
    3. (c)$4952$ cm${}^2$
    4. (d)$4953$ cm${}^2$
    Show answer

    (a) $4950$ cm${}^2$

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14. Q14
    A ​medicine-capsule is in the shape of a cylinder of ​diameter ​0.5 cm with two ​hemispheres stuck to each of its ends. ​The length of ​entire ​capsule is 2 cm. The capacity of the ​capsule is

    1. (a)$0.36{\text{cm}}^3$
    2. (b)$0.35{\text{cm}}^3$
    3. (c)$0.34{\text{cm}}^3$
    4. (d)$0.33{\text{cm}}^3$
    Show answer

    (a) $0.36{\text{cm}}^3$

    Step-by-step solution →
15. Q15
    If two ​solid hemispheres of same ​base radius $r$ are joined ​together along their bases, then ​curved ​surface area ​of this ​new solid is

    1. (a)$4\pi r^2$
    2. (b)$6\pi r^2$
    3. (c)$3\pi r^2$
    4. (d)$8\pi r^2$
    Show answer

    (a) $4\pi r^2$

    Step-by-step solution →
16. Q16
    A right circular ​cylinder of ​radius $r$ cm ​and height $h$ ​cm ($h>2r$) ​just ​encloses ​a sphere of diameter

    1. (a)$r$ cm
    2. (b)$2r$ cm
    3. (c)$h$ cm
    4. (d)$2h$ cm
    Show answer

    (b) $2r$ cm

    Step-by-step solution →
17. Q17
    During conversion ​of ​a ​solid from ​one shape ​to another, the volume of the new shape ​will

    1. (a)increase
    2. (b)decrease
    3. (c)remain unaltered
    4. (d)be doubled
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    (c) remain unaltered

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18. Q18
    The ​diameters of the ​two circular ends of the bucket ​are 44 ​cm and 24 cm. The height of the bucket ​is ​35 cm. ​The capacity of the bucket ​is

    1. (a)$32.7$ litres
    2. (b)$33.7$ litres
    3. (c)$34.7$ litres
    4. (d)$31.7$ litres
    Show answer

    (a) $32.7$ litres

    Step-by-step solution →
19. Q19
    In a right ​circular cone, the cross-section made ​by ​a plane ​parallel to the ​base is a

    1. (a)circle
    2. (b)frustum of a cone
    3. (c)sphere
    4. (d)hemisphere
    Show answer

    (a) circle

    Step-by-step solution →
20. Q20
    Volumes of two ​spheres ​are in ​the ratio ​64:27. The ​ratio of ​their surface areas is

    1. (a)3 : 4
    2. (b)4 : 3
    3. (c)9 : 16
    4. (d)16 : 9
    Show answer

    (d) 16 : 9

    Step-by-step solution →