Class 10 Maths · Chapter 12

Surface Areas and Volumes

110 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 5 of 6

1. Q81 CBSE 2026
   A ​cylinder ​of radius $r$ ​is surmounted ​on a hemisphere of same radius. ​If total height of ​the object is $13$ cm, ​then its inner surface area is

   1. (a)$2\pi r(r+13)$
   2. (b)$13\pi r$
   3. (c)$2\pi (13+r{)}^2$
   4. (d)$26\pi r$
   Show answer

   (d) $26\pi r$

   Step-by-step solution →
2. Q82 CBSE 2026
   A ​cone ​of maximum size is carved out ​from a solid cube of ​edge length $l$. The ​volume of the cone ​is ​:

   1. (a)$\frac{\pi l^3}{12}$
   2. (b)$\frac{\pi l^3}{3}$
   3. (c)$l^3\left(1-\frac{\pi }{3}\right)$
   4. (d)$\frac{\pi l^3}{8}$
   Show answer

   (a) $\frac{\pi l^3}{12}$

   Step-by-step solution →
3. Q83 CBSE 2026
   A conical cavity ​of maximum ​volume is ​carved out from a ​wooden ​solid hemisphere of radius $10$ cm. Curved surface area of ​the ​cavity carved out is ​(use $\pi =3.14$)

   1. (a)$314\sqrt{2}{\text{cm}}^2$
   2. (b)$314{\text{cm}}^2$
   3. (c)$\frac{3140}{3}{\text{cm}}^2$
   4. (d)$3140\sqrt{2}{\text{cm}}^2$
   Show answer

   (a) $314\sqrt{2}{\text{cm}}^2$

   Step-by-step solution →
4. Q84 CBSE 2026
   A cone with slant height $10$ cm and radius $6$ cm ​is surmounted ​on ​a ​hemisphere ​of the same radius. ​The height of the toy ​is:

   1. (a)$12$ cm
   2. (b)$16$ cm
   3. (c)$14$ cm
   4. (d)$10$ cm
   Show answer

   (c) $14$ cm

   Step-by-step solution →
5. Q85 CBSE 2026
   A ​camping tent in hemispherical shape of ​radius $1.4$ ​m, has a door opening of area $0.50$ m${}^2$. Outer ​surface area of ​the tent is ​:

   1. (a)$11.78$ m${}^2$
   2. (b)$12.32$ m${}^2$
   3. (c)$11.82$ m${}^2$
   4. (d)$12.86$ m${}^2$
   Show answer

   (c) $11.82$ m${}^2$

   Step-by-step solution →
6. Q86 CBSE 2026
   Three tennis balls ​are just packed in a cylindrical jar. If ​radius ​of each ​ball is $r$, volume of air ​inside the ​jar ​is

   1. (a)$2\pi r^3$
   2. (b)$3\pi r^3$
   3. (c)$5\pi r^3$
   4. (d)$4\pi r^3$
   Show answer

   (a) $2\pi r^3$

   Step-by-step solution →
7. Q87 CBSE 2026
   The ​number of ​conical bottles of radius $2$ cm and height $1.2$ cm that can be ​filled from ​a cylindrical bottle of radius $6$ cm ​and height $8$ ​cm, full of liquid, is

   1. (a)$60$
   2. (b)$130$
   3. (c)$180$
   4. (d)$18$
   Show answer

   (c) $180$

   Step-by-step solution →
8. Q88 CBSE 2026
   The ​largest possible right ​circular ​cone ​is carved out of a solid hemisphere ​of radius '$r$' as ​shown in the figure below. ​The slant height of the cone is :

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

   (c) $\sqrt{2}r$

   Step-by-step solution →
9. Q89 CBSE 2026
   The ​radius of the largest sphere ​that can be ​carved out from a solid ​cube of ​side $14$ ​cm is :

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

   (a) $7$ cm

   Step-by-step solution →
10. Q90 CBSE 2026
    The ​total surface ​area of a solid hemisphere of ​diameter ​'$2d$' ​is ​:

    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

    (a) $3\pi d^2$

    Step-by-step solution →
11. Q91 CBSE 2026
    A hemispherical bowl ​is made of steel of thickness $1$ ​cm. The outer ​radius of the bowl is $6$ cm. The volume ​of steel ​used (in ${\text{cm}}^3$) 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. Q92 CBSE 2026
    Volumes ​of two spheres are in the ​ratio $64:27$. The ​ratio of ​their surface ​areas is:

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

    (c) $16:9$

    Step-by-step solution →
13. Q93 CBSE 2026
    An ​ice-cream ​cone of radius $r$ ​and height $h$ is completely ​filled by two spherical scoops ​of ​ice-cream. ​If the radius of each ​spherical scoop is $\frac{r}{2}$, then $h:2r$ equals :

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

    (b) $1:2$

    Step-by-step solution →
14. Q94 CBSE 2026
    In the ​adjoining ​figure, the ​slant ​height of ​the conical ​part is ​:

    1. (a)$4$ cm
    2. (b)$7$ cm
    3. (c)$5$ cm
    4. (d)$25$ cm
    Show answer

    (c) $5$ cm

    Step-by-step solution →
15. Q95 CBSE 2026
    The ​total surface area ​of a ​solid cone of ​radius $7$ cm ​and slant height $25$ ​cm, is

    1. (a)$724{\text{cm}}^2$
    2. (b)$704{\text{cm}}^2$
    3. (c)$550{\text{cm}}^2$
    4. (d)$616{\text{cm}}^2$
    Show answer

    (b) $704{\text{cm}}^2$

    Step-by-step solution →
16. Q96 CBSE 2026
    In ​the following question, ​a ​statement of Assertion (A) ​is ​followed by a statement ​of Reason ​(R). Choose the correct option ​:

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

    Reason (R): The 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 →
17. Q97 CBSE 2026
    A ​toy is in ​the form of ​a cone mounted on ​a hemisphere of ​radius $7$ cm. The total height of the ​toy is $31$ cm. Find the total surface area of the toy.

    Show answer

    The total surface area of the toy is $273\pi =858{\text{cm}}^2$.

    Step-by-step solution →
18. Q98 CBSE 2026
    To ​protect plants from heat, a shed of iron rods ​covered with green cloth is ​made. The lower part of ​the shed is ​a cuboid mounted by semi-cylinder as shown in the figure. Find the area of ​the cloth required to make this shed, if dimensions of the cuboid ​are $14\text{ m}\times 25\text{ m}\times 16\text{ m}$.

    Show answer

    The area of the cloth required to make the shed is $1952{\text{m}}^2$.

    Step-by-step solution →
19. Q99 CBSE 2026
    The internal and ​external radii of a hollow hemisphere are $5\sqrt{2}$ cm ​and $10$ ​cm respectively. A cone of height $5\sqrt{7}$ cm ​and ​radius $5\sqrt{2}$ cm is ​surmounted ​on the hemisphere as shown in the figure. Find the total surface area of ​the object in terms of $\pi$. (Use $\sqrt{2}=1.4$)

    Show answer

    The total surface area of the object is $355\pi$ cm${}^2$.

    Step-by-step solution →
20. Q100 CBSE 2026
    A solid is in the ​form of a cylinder with hemispherical ends. The total ​height of ​the solid is $20$ cm and the diameter of the cylinder is $7$ cm. Find ​the total volume ​of ​the ​solid. $\left(\text{Use }\pi =\frac{22}{7}\right)$
    Show answer

    The total volume of the solid is $\frac{4081}{6}$ cm${}^3$, which is approximately $680.17$ cm${}^3$.

    Step-by-step solution →