Class 10 Maths · Chapter 12

Surface Areas and Volumes

393 Class 10 Maths questions on Surface Areas and Volumes from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 9 of 20

1. Q161 CBSE 2024
   The ​radius of ​a sphere is $\frac{7}{2}$ cm. The ​volume of ​the ​sphere is:

   1. (a)$\frac{231}{3}$ cu cm
   2. (b)$\frac{539}{12}$ cu cm
   3. (c)$\frac{539}{3}$ cu cm
   4. (d)$154$ cu cm
   Show answer

   (c) $\frac{539}{3}$ cu cm

   Step-by-step solution →
2. Q162 CBSE 2024
   The ​total ​surface ​area ​of a ​solid hemisphere of ​radius $7$ cm is ​:

   1. (a)$98\pi {\text{cm}}^2$
   2. (b)$147\pi {\text{cm}}^2$
   3. (c)$196\pi {\text{cm}}^2$
   4. (d)$228\frac{2}{3}\pi {\text{cm}}^2$
   Show answer

   (b) $147\pi {\text{cm}}^2$

   Step-by-step solution →
3. Q163 CBSE 2024
   A ​solid ​sphere is cut into two ​hemispheres. The ratio of the surface ​areas of ​sphere to that of two hemispheres taken together, is :

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

   (c) $2:3$

   Step-by-step solution →
4. Q164 CBSE 2024
   The height and radius ​of a ​right ​circular cone ​are $24$ cm and $7$ cm respectively. The ​slant height ​of the cone is:

   1. (a)$24$ cm
   2. (b)$31$ cm
   3. (c)$26$ cm
   4. (d)$25$ cm
   Show answer

   (d) $25$ cm

   Step-by-step solution →
5. Q165 CBSE 2024
   The ​volume of ​the largest right circular cone ​that ​can be ​carved out ​from a solid cube of edge $2$ cm is ​:

   1. (a)$\frac{4\pi }{3}$ cu cm
   2. (b)$\frac{5\pi }{3}$ cu cm
   3. (c)$\frac{8\pi }{3}$ cu cm
   4. (d)$\frac{2\pi }{3}$ cu cm
   Show answer

   (d) $\frac{2\pi }{3}$ cu cm

   Step-by-step solution →
6. Q166 CBSE 2024
   From a ​solid ​cube of ​side $14$ cm, a ​sphere of maximum ​diameter is ​carved out. ​The radius ​of sphere is :

   1. (a)$7$ cm
   2. (b)$14$ cm
   3. (c)$\frac{7}{2}$ cm
   4. (d)$\sqrt{14}$ cm
   Show answer

   (a) $7$ cm

   Step-by-step solution →
7. Q167 CBSE 2024
   If the ​volumes of ​two ​spheres ​are in the ratio $125:64$, then ​the ratio of their surface areas is ​:

   1. (a)$5:4$
   2. (b)$25:16$
   3. (c)$125:64$
   4. (d)$16:5$
   Show answer

   (b) $25:16$

   Step-by-step solution →
8. Q168 CBSE 2024
   If the volume ​of ​a sphere ​of radius $R$ is equal to $16$ ​times the ​volume of a hemisphere ​of radius $r$, ​then $R:r$ is :

   1. (a)1 : 2
   2. (b)2 : 1
   3. (c)8 : 1
   4. (d)1 : 8
   Show answer

   (b) 2 : 1

   Step-by-step solution →
9. Q169 CBSE 2024
   Two cubes each ​of volume $64$ ​cm${}^3$ ​are ​joined ​end ​to end to form a cuboid. The ​total surface area of ​the resulting cuboid is :

   1. (a)$192$ cm${}^2$
   2. (b)$160$ cm${}^2$
   3. (c)$128$ cm${}^2$
   4. (d)$176$ cm${}^2$
   Show answer

   (b) $160$ cm${}^2$

   Step-by-step solution →
10. Q170 CBSE 2024
    A solid is ​hemispherical ​at the bottom and ​conical ​above (of same radius). If the ​curved surface areas of the two parts are equal, then the ratio of its radius and the height ​of ​the conical part is:

    1. (a)$1:3$
    2. (b)$3:1$
    3. (c)$\sqrt{3}:1$
    4. (d)$1:\sqrt{3}$
    Show answer

    (d) $1:\sqrt{3}$

    Step-by-step solution →
11. Q171 CBSE 2024
    Read ​the Assertion ​(A) ​and ​Reason ​(R) ​and choose the ​correct option.

    Assertion (A): The volume of a cone of radius $7$ cm and height $12$ cm is $616$ cm${}^3$.

    Reason (R): The volume of a cone is $\frac{1}{3}\pi r^{2}h$, (where $r$ is radius and $h$ is the height).

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
12. Q172 CBSE 2024
    Directions: A statement of Assertion (A) ​is followed ​by a statement ​of ​Reason ​(R). Choose ​the correct option.

    Assertion (A): Two cubes each with 12 cm edge are joined end to end. The surface area of the resulting cuboid $=2\times$ (surface area of one cube).

    Reason (R): The surface area of a cuboid $=2(lb+bh+hl)$, where $l$, $b$, $h$ respectively are its length, breadth and height.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (d) Assertion (A) is false, but Reason (R) is true.

    Step-by-step solution →
13. Q173 CBSE 2024
    Assertion (A): If surface areas ​of two spheres are ​in ​the ratio $16:9$, ​then their volumes are in the ​ratio $64:27$. Reason ​(R): ​If $S_1$ and $S_2$ are the surface areas of two spheres ​and $V_1$ and $V_2$ are their volumes respectively, then $\frac{V_1}{V_2}={\left(\frac{S_1}{S_2}\right)}^{3/2}$.

    Assertion (A): If surface areas of two spheres are in the ratio $16:9$, then their volumes are in the ratio $64:27$.

    Reason (R): If $S_1$ and $S_2$ are the surface areas of two spheres and $V_1$ and $V_2$ are their volumes respectively, then $\frac{V_1}{V_2}={\left(\frac{S_1}{S_2}\right)}^{3/2}$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
14. Q174 CBSE 2024
    Two statements ​are given - one labelled ​Assertion ​(A) and the other ​labelled ​Reason (R). ​Select ​the correct option.

    Assertion (A): The area of canvas cloth required to just cover a heap of rice in the form of a cone of diameter 14 m and height 24 m is $175\pi$ sq.m.

    Reason (R): The curved surface area of a cone of radius r and slant height $l$ is $\pi rl$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
15. Q175 CBSE 2024
    Choose ​the correct ​option for ​the following ​Assertion (A) and ​Reason (R).

    Assertion (A): Two cubes each of edge length $10$ cm are joined together. The total surface area of the newly formed cuboid is $1200$ cm${}^2$.

    Reason (R): Area of each surface of a cube of side $10$ cm is $100$ cm${}^2$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (d) Assertion (A) is false, but Reason (R) is true.

    Step-by-step solution →
16. Q176 CBSE 2024
    A vessel is in the form of ​a hollow ​hemisphere surmounted by a hollow cylinder. The diameter ​of the hemisphere is $14$ ​cm and ​the total height of the ​vessel is $13$ cm. Find the ​inner surface area of the vessel.
    Show answer

    The inner surface area of the vessel is $572$ cm${}^2$.

    Step-by-step solution →
17. Q177 CBSE 2024
    A solid toy is in the ​form of a ​hemisphere surmounted by a ​right ​circular cone. The ​height of the cone is $2$ cm ​and the diameter of the base ​is $4$ ​cm. Determine the volume of the toy.
    Show answer

    Volume of the toy $=8\pi$ cm${}^3$ $=\frac{176}{7}\approx 25.14$ cm${}^3$ (taking $\pi =\frac{22}{7}$).

    Step-by-step solution →
18. Q178 CBSE 2024
    From a ​solid cone, whose height is ​16 cm ​and radius 12 cm, a ​conical cavity of height 3 cm and base ​radius 4 cm is ​hollowed out such that ​the bases of the cones form ​concentric circles. Find the total surface area of the remaining solid.
    Show answer

    Total surface area of the remaining solid $=388\pi$ cm² $=\frac{8536}{7}\approx 1219.43$ cm² (taking $\pi =\frac{22}{7}$).

    Step-by-step solution →
19. Q179 CBSE 2024
    A solid is ​in the form ​of ​a cylinder with hemi-spherical ends of same radii. The total height of the solid is $20$ cm ​and the diameter of ​the cylinder is $14$ ​cm. Find the surface ​area of the ​solid.
    Show answer

    Surface area of the solid $=880{\text{cm}}^2$.

    Step-by-step solution →
20. Q180 CBSE 2024
    A juice glass is ​cylindrical in ​shape with ​hemi-spherical ​raised up portion at the bottom. The inner ​diameter of glass is $10$ cm and its ​height is $14$ ​cm. ​Find the capacity of the glass. (use $\pi =3.14$)
    Show answer

    Capacity of the glass $=\frac{2512}{3}{\text{cm}}^3\approx 837.33{\text{cm}}^3$.

    Step-by-step solution →