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 7 of 20

1. Q121 CBSE 2025
   The curved surface ​area of a cone ​with base ​radius $7$ ​cm, is $550{\text{ cm}}^2$. The slant ​height of ​the cone ​is ​:

   1. (a)$25$ cm
   2. (b)$14$ cm
   3. (c)$20$ cm
   4. (d)$24$ cm
   Show answer

   (a) $25$ cm

   Step-by-step solution →
2. Q122 CBSE 2025
   A cone and a cylinder ​have the same ​base radius ​and volume. The (height of ​cone ​: height of cylinder) ​is :

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

   (b) $3:1$

   Step-by-step solution →
3. Q123 CBSE 2025
   A cone ​and cylinder ​have same height and same radius. The ​volume ​of the cone and ​the volume of the cylinder are ​in the ratio :

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

   (b) $1:3$

   Step-by-step solution →
4. Q124 CBSE 2025
   The total ​surface ​area ​of ​a solid ​hemisphere of radius $7$ cm is

   1. (a)$98\pi {\text{ cm}}^2$
   2. (b)$196\pi {\text{ cm}}^2$
   3. (c)$147\pi {\text{ cm}}^2$
   4. (d)$174\pi {\text{ cm}}^2$
   Show answer

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

   Step-by-step solution →
5. Q125 CBSE 2025
   The volume of ​air in ​a hollow cylinder ​is $450{\text{cm}}^3$. A cone ​of the same height and radius as the ​cylinder is kept inside it. The volume of the empty ​space ​in the cylinder is

   1. (a)$225$ cm${}^3$
   2. (b)$150$ cm${}^3$
   3. (c)$250$ cm${}^3$
   4. (d)$300$ cm${}^3$
   Show answer

   (d) $300$ cm${}^3$

   Step-by-step solution →
6. Q126 CBSE 2025
   Directions: In the following question, a ​statement ​of ​Assertion ​(A) is followed by a statement of Reason ​(R). Choose ​the correct ​option.

   Assertion (A): In the given figure, a toy is in the form of a cylinder surmounted by a hemisphere of the same radius. If the radius of the cylinder is 3 cm and its height is 7 cm, then the volume of toy is $81\pi {\text{cm}}^3$.

   Reason (R): Volume of the given solid is the sum of the volume of the cylinder and the volume of the hemisphere.

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

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

   Step-by-step solution →
7. Q127 CBSE 2025
   Read the ​assertion ​and ​reason and ​choose ​the ​correct ​option.

   Assertion (A): When a hemisphere of same radius ($r$) is carved out from one side of a solid wooden cylinder, the total surface area of remaining solid is increased by $2\pi r^2$.

   Reason (R): Curved surface area of hemisphere is $2\pi r^2$.

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

   (d) A is false but R is true.

   Step-by-step solution →
8. Q128 CBSE 2025
   Read the ​assertion and reason ​and ​choose ​the correct ​option.

   Assertion (A): The curved surface area of a right circular cone of radius $3.5$ cm and slant height $4$ cm is $44$ sq cm.

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

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

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

   Step-by-step solution →
9. Q129 CBSE 2025
   In the ​following question, ​a statement ​of Assertion (A) is followed ​by a statement of ​Reason (R). Choose the correct option.

   Assertion (A): If we join two hemispheres of same radius along their bases, then we get a sphere.

   Reason (R): Total Surface Area of a sphere of radius $r$ is $3\pi r^2$.

   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

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

   Step-by-step solution →
10. Q130 CBSE 2025
    Read the ​Assertion (A) ​and ​Reason (R) ​carefully and ​choose ​the correct option.

    Assertion (A): If the total surface area of a solid hemisphere is $462$ cm${}^2$, then its radius is $7$ cm.

    Reason (R): The total surface area of a solid hemisphere of radius $r$ is $3\pi r^2$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 the Assertion (A).

    Step-by-step solution →
11. Q131 CBSE 2025
    A ​room is ​in the ​form of a ​cylinder ​surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If ​the room contains $\frac{1408}{21}$ m${}^3$ of ​air, ​find the height of the cylindrical part. (Use $\pi =\frac{22}{7}$.)
    Show answer

    The height of the cylindrical part of the room is $4$ m.

    Step-by-step solution →
12. Q132 CBSE 2025
    A ​spherical glass vessel has ​a ​cylindrical neck $7$ ​cm long and $8$ cm ​in diameter. The ​radius ​of spherical part is $10$ cm. Find the volume of the vessel.
    Show answer

    Volume of the vessel $=\frac{95392}{21}\approx 4542.48$ cm³.

    Step-by-step solution →
13. Q133 CBSE 2025
    From each end of a ​solid ​cylinder ​of height $20$ cm and base radius $7$ ​cm, a ​cone of base radius $2.1$ cm and height $5$ cm is scooped out. Find the volume of ​the remaining solid.
    Show answer

    Volume of the remaining solid $=3033.8{\text{cm}}^3$.

    Step-by-step solution →
14. Q134 CBSE 2025
    A ​spherical glass vessel has a cylindrical neck $8$ ​cm long, $2$ ​cm in ​diameter; the diameter ​of the spherical part is $8.5$ cm. Find the amount of water it can ​hold, when it is full up to the top. ​Also, find its external curved surface ​area. [Use $\pi =3.14$.]
    Show answer

    The vessel holds about $346.51{\text{cm}}^3$ of water, and its external curved surface area is about $277.11{\text{cm}}^2$.

    Step-by-step solution →
15. Q135 CBSE 2025
    A toy ​is ​in the form ​of a cone of radius $3.5$ cm, ​mounted on ​a hemisphere of same radius. ​The ​total height of the toy is $15.5$ cm. Find the total ​surface area of the toy.
    Show answer

    The total surface area of the toy is $214.5{\text{cm}}^2$.

    Step-by-step solution →
16. Q136 CBSE 2025
    A perfume bottle is in the form of a cylinder ​but the bottom of ​the bottle has a hemispherical raised portion to ​reduce the ​capacity of the bottle. The inner diameter of the bottle is $5$ cm ​and the height of the bottle is $10$ cm. Find the capacity of the perfume bottle ​in mL. (Use $\pi =3.14$ and $1$ cm${}^3=1$ mL)

    Show answer

    Capacity of the perfume bottle $\approx 163.54$ mL.

    Step-by-step solution →
17. Q137 CBSE 2025
    A wooden cubical die is ​formed by forming hemispherical depressions on each face of ​the cube such that face 1 has one depression, face 2 has two ​depressions ​and so on. The ​sum of number of hemispherical depressions on opposite faces is always $7$. If the edge of the cubical die measures $5$ cm and each hemispherical depression is of diameter $1.4$ cm, ​find the total surface area of the die so formed.
    Show answer

    The total surface area of the die so formed is $182.34{\text{cm}}^2$.

    Step-by-step solution →
18. Q138 CBSE 2025
    A toy ​is ​in the form of a ​cone of radius $3.5$ cm mounted on a hemisphere of ​the same ​radius. The total height ​of the toy is $15.5$ cm. Find the surface area of the toy.
    Show answer

    The surface area of the toy is $214.5{\text{cm}}^2$.

    Step-by-step solution →
19. Q139 CBSE 2025
    A wooden article was ​made by scooping ​out a hemisphere (of same diameter) from one end of a solid cylinder as shown in the given ​figure. If the height of ​the cylinder is $10$ ​cm and the diameter of the cylinder is $14$ cm, find ​the total surface ​area of the ​remaining wooden article. (Use $\pi =\frac{22}{7}$)

    Show answer

    The total surface area of the remaining wooden article is $902{\text{cm}}^2$.

    Step-by-step solution →
20. Q140 CBSE 2025
    From one ​face of a solid ​cube of side $14$ cm, the ​largest possible cone is carved out. Find the volume ​and ​surface area of the ​remaining ​solid. (Use $\pi =\frac{22}{7}$, $\sqrt{5}=2.2$)
    Show answer

    The volume of the remaining solid is $\frac{6076}{3}{\text{cm}}^3$ (about $2025.33{\text{cm}}^3$) and its surface area is $1360.8{\text{cm}}^2$.

    Step-by-step solution →