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 11 of 20

1. Q201 CBSE 2023
   Total ​surface ​area (internal and external) of a ​hemispherical ​bowl ​having ​radii $r_1$ and $r_2$ ($r_2>r_1$) ​is:

   1. (a)$2\pi (r_1^2+r_2^2)$
   2. (b)$\pi (r_1^2+r_2^2)$
   3. (c)$3\pi r_2^2+\pi r_1^2$
   4. (d)$3\pi r_1^2+\pi r_2^2$
   Show answer

   (c) $3\pi r_2^2+\pi r_1^2$

   Step-by-step solution →
2. Q202 CBSE 2023
   The curved surface area of ​a right ​circular cylinder of ​height $14$ cm is $88$ cm${}^2$. The diameter of its circular ​base ​is ​:

   1. (a)$2$ cm
   2. (b)$1$ cm
   3. (c)$4$ cm
   4. (d)$7$ cm
   Show answer

   (a) $2$ cm

   Step-by-step solution →
3. Q203 CBSE 2023
   Water in a river which is $3$ m deep and $40$ ​m ​wide is ​flowing ​at the rate ​of $2$ km/h. How much ​water will fall ​into ​the sea in $2$ minutes ?

   1. (a)$800$ m${}^3$
   2. (b)$4000$ m${}^3$
   3. (c)$8000$ m${}^3$
   4. (d)$2000$ m${}^3$
   Show answer

   (c) $8000$ m${}^3$

   Step-by-step solution →
4. Q204 CBSE 2023
   What ​is the ​total surface ​area of ​a ​solid hemisphere of ​diameter $d$?

   1. (a)$3\pi d^2$
   2. (b)$2\pi d^2$
   3. (c)$\frac{1}{2}\pi d^2$
   4. (d)$\frac{3}{4}\pi d^2$
   Show answer

   (d) $\frac{3}{4}\pi d^2$

   Step-by-step solution →
5. Q205 CBSE 2023
   Curved ​surface ​area of a ​cylinder ​of height $5$ cm is $94.2$ cm${}^2$. Radius ​of the ​cylinder ​is (Take $\pi =3.14$)

   1. (a)$2$ cm
   2. (b)$3$ cm
   3. (c)$2.9$ cm
   4. (d)$6$ cm
   Show answer

   (b) $3$ cm

   Step-by-step solution →
6. Q206 CBSE 2023
   A solid is of the form of ​a cone of radius ​'r' surmounted on a hemisphere of the same radius. If the height ​of ​the cone is the same as the diameter ​of its base, then the volume of the ​solid ​is :

   1. (a)$\pi r^3$
   2. (b)$\frac{4}{3}\pi r^3$
   3. (c)$3\pi r^3$
   4. (d)$\frac{2}{3}\pi r^3$
   Show answer

   (b) $\frac{4}{3}\pi r^3$

   Step-by-step solution →
7. Q207 CBSE 2023
   Two cubes ​each of $5$ ​cm edge ​are joined end to ​end. The surface ​area ​of the resulting cuboid is:

   1. (a)$200$ cm${}^2$
   2. (b)$300$ cm${}^2$
   3. (c)$125$ cm${}^2$
   4. (d)$250$ cm${}^2$
   Show answer

   (d) $250$ cm${}^2$

   Step-by-step solution →
8. Q208 CBSE 2023
   The ​volume ​of a ​right circular cone whose area of the ​base is $156$ cm${}^2$ ​and the vertical ​height is $8$ ​cm, is

   1. (a)$2496$ cm${}^3$
   2. (b)$1248$ cm${}^3$
   3. (c)$1664$ cm${}^3$
   4. (d)$416$ cm${}^3$
   Show answer

   (d) $416$ cm${}^3$

   Step-by-step solution →
9. Q209 CBSE 2023
   The ​curved ​surface ​area ​of ​a cone having ​height $24$ cm and ​radius $7$ cm, is

   1. (a)$528$ cm${}^2$
   2. (b)$1056$ cm${}^2$
   3. (c)$550$ cm${}^2$
   4. (d)$500$ cm${}^2$
   Show answer

   (c) $550$ cm${}^2$

   Step-by-step solution →
10. Q210 CBSE 2023
    The volume of ​a ​cone ​of ​radius $r$ ​and ​height $3r$ ​is:

    1. (a)$\frac{1}{3}\pi r^3$
    2. (b)$3\pi r^3$
    3. (c)$9\pi r^3$
    4. (d)$\pi r^3$
    Show answer

    (d) $\pi r^3$

    Step-by-step solution →
11. Q211 CBSE 2023
    A hemispherical bowl is ​made of steel of thickness $1$ cm. ​The inner ​radius ​of the bowl is $5$ cm. The volume of steel ​used (in ​cm${}^3$) is:

    1. (a)$182\pi$
    2. (b)$\frac{182}{3}\pi$
    3. (c)$\frac{682}{3}\pi$
    4. (d)$\frac{364}{3}\pi$
    Show answer

    (b) $\frac{182}{3}\pi$

    Step-by-step solution →
12. Q212 CBSE 2023
    A ​'top' is of ​the ​shape ​of a cone mounted over a hemisphere of same radius. The radius ​of hemisphere is $3.5$ cm and the total height of the top ​is $15.5$ ​cm. The total surface area of the 'top' ​(in cm${}^2$) is :

    1. (a)$2145$
    2. (b)$21.45$
    3. (c)$215.4$
    4. (d)$214.5$
    Show answer

    (d) $214.5$

    Step-by-step solution →
13. Q213 CBSE 2023
    A solid hemisphere ​of radius $r$ is surmounted by ​a ​solid cone ​of same base radius ​as that ​of the hemisphere and height equal to ​its diameter. The volume of this combined solid is ​:

    1. (a)$\pi r^3$
    2. (b)$\frac{2}{3}\pi r^3$
    3. (c)$\frac{1}{3}\pi r^3$
    4. (d)$\frac{4}{3}\pi r^3$
    Show answer

    (d) $\frac{4}{3}\pi r^3$

    Step-by-step solution →
14. Q214 CBSE 2023
    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)$4:5$
    3. (c)$16:25$
    4. (d)$25:16$
    Show answer

    (d) $25:16$

    Step-by-step solution →
15. Q215 CBSE 2023
    Read the Assertion ​(A) and Reason ​(R) below and ​choose ​the ​correct option.

    Assertion (A): The surface area of the cuboid formed by joining two cubes of sides $4$ cm each, end to end, is $160$ cm${}^2$.

    Reason (R): Surface area of a cuboid of dimensions $l\times b\times h$ is $(lb+bh+hl)$.

    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 →
16. Q216 CBSE 2023
    Assertion (A): The diameter of a sphere, whose surface area is $616{\text{cm}}^2$, is 7 cm.

    Reason (R): The surface area of a sphere of radius $r$ is $4\pi r^2$.

    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 →
17. Q217 CBSE 2023
    Assertion (A): The surface area of largest sphere that can be inscribed in a hollow cube of side 'a' cm is $\pi a^2$ cm${}^2$.

    Reason (R): The surface area of a sphere of radius 'r' is $\frac{4}{3}\pi r^3$.

    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 →
18. Q218 CBSE 2023
    A ​room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius ​of hemisphere is one-half the height ​of ​cylindrical part. ​Find total height of the room if ​it ​contains $\left(\frac{1408}{21}\right)$ m${}^3$ of air. $\left(\text{Take }\pi =\frac{22}{7}\right)$
    Show answer

    The total height of the room is $6$ m.

    Step-by-step solution →
19. Q219 CBSE 2023
    $3$ cubes ​each ​of volume $64$ cm${}^3$ ​are ​joined end-to-end to form a ​cuboid. Find the surface area ​of this ​cuboid.
    Show answer

    Surface area $=224$ cm${}^2$

    Step-by-step solution →
20. Q220 CBSE 2023
    An empty cone is of radius $3$ cm and ​height $12$ ​cm. Ice-cream is filled in it so that ​lower part of ​the cone which is ${\left(\frac{1}{6}\right)}^{th}$ of the ​volume of the ​cone is unfilled but hemisphere is formed ​on the top. Find volume ​of the ice-cream. $\left(\text{Take }\pi =3.14\right)$

    Show answer

    The volume of the ice-cream is $150.72$ cm${}^3$.

    Step-by-step solution →