Class 10 Maths · Chapter 12

Surface Areas and Volumes

90 Class 10 Maths questions on Surface Areas and Volumes from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 5

1. Q21 Exemplar · Exercise 12.1
   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 →
2. Q22 Exemplar · Exercise 12.1
   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 →
3. Q23 Exemplar · Exercise 12.1
   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 →
4. Q24 Exemplar · Exercise 12.1
   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 →
5. Q25 Exemplar · Exercise 12.1
   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

   Step-by-step solution →
6. Q26 Exemplar · Exercise 12.1
   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 →
7. Q27 Exemplar · Exercise 12.1
   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 →
8. Q28 Exemplar · Exercise 12.1
   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 →
9. Q29 Exemplar · Exercise 12.1
   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
   Show answer

   (c) 2 cm

   Step-by-step solution →
10. Q30 Exemplar · Exercise 12.1
    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${}^2$

    Step-by-step solution →
11. Q31 Exemplar · Exercise 12.1
    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 →
12. Q32 Exemplar · Exercise 12.1
    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 →
13. Q33 Exemplar · Exercise 12.1
    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 →
14. Q34 Exemplar · Exercise 12.1
    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
    Show answer

    (c) remain unaltered

    Step-by-step solution →
15. Q35 Exemplar · Exercise 12.1
    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 →
16. Q36 Exemplar · Exercise 12.1
    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 →
17. Q37 Exemplar · Exercise 12.1
    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 →
18. Q38 Exemplar · Exercise 12.2
    Two identical solid hemispheres of equal base ​radius $r$ cm are stuck ​together along their ​bases. The ​total ​surface area of ​the combination is $6\pi r^2$.
    Show answer

    False

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19. Q39 Exemplar · Exercise 12.2
    Write 'True' or 'False' ​and justify ​your answer: A solid ​cylinder of radius $r$ and height $h$ is placed over another ​cylinder ​of same height ​and radius. ​The total surface area of the shape ​so formed is $4\pi rh+4\pi r^2$.
    Show answer

    False

    Step-by-step solution →
20. Q40 Exemplar · Exercise 12.2
    A solid cone of radius $r$ and ​height $h$ is placed over a ​solid cylinder having ​same ​base ​radius and height as that ​of a cone. The total surface area ​of the combined ​solid is $\pi r\left[\sqrt{r^2+h^2}+3r+2h\right]$.
    Show answer

    False

    Step-by-step solution →