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 17 of 20

1. Q321 CBSE 2018
   A cylinder ​whose height is two-third of its ​diameter, has the same volume ​as that of ​a sphere of radius $4$ ​cm. ​Find the radius of base of the ​cylinder.
   Show answer

   Radius of base of the cylinder $r=4$ cm.

   Step-by-step solution →
2. Q322 CBSE 2018
   The diameters of the lower and ​upper ends of a ​bucket in the form of a frustum of ​a cone are $10$ cm and $30$ cm respectively. If its height ​is $24$ cm, find :

   1. (i)The area of the metal sheet used ​to make the ​bucket.
   2. (ii)Why ​we should avoid ​the bucket made by ordinary plastic ? [Use $\pi =3.14$]

   1. iThe area of the metal sheet used to make the bucket.
   2. iiWhy we should avoid the bucket made by ordinary plastic ?
   Show answer

   (i) Metal sheet area $=\pi (R+r)l+\pi r^2=1632.8+78.5=1711.3$ cm${}^2$. (ii) Ordinary plastic is non-biodegradable and pollutes the environment, so such buckets should be avoided.

   Step-by-step solution →
3. Q323 CBSE 2018
   The ​diameters of ​the lower and ​upper ends of a ​bucket in the form of a ​frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

   1. (i)The area of the metal sheet used ​to make the bucket.
   2. (ii)Why we ​should avoid the bucket made by ordinary plastic? [Use $\pi =3.14$]

   1. (i)The area of the metal sheet used to make the bucket.
   2. (ii)Why we should avoid the bucket made by ordinary plastic?
   Show answer

   (i) The area of the metal sheet is $1711.3$ cm². (ii) Ordinary plastic is non-biodegradable and pollutes the environment, so such buckets should be avoided in favour of eco-friendly materials.

   Step-by-step solution →
4. Q324 CBSE 2018
   Sudhakar donated $3$ cylindrical ​drums ​to store cereals to an orphanage. If radius of each drum is $0.7$ m and height $2$ m, find the volume of each ​drum. If each drum ​costs $\text{₹}350$ per m${}^3$, find the amount ​spent by Sudhakar for orphanage. What value is exhibited ​in ​the question. (Use $\pi =\frac{22}{7}$)
   Show answer

   Each drum $=3.08$ m${}^3$; total amount spent $=\text{₹}3234$. Value exhibited: generosity / kindness / helping the needy.

   Step-by-step solution →
5. Q325 CBSE 2017
   Volume ​and surface ​area of a ​solid hemisphere are numerically equal. ​What ​is ​the diameter of hemisphere?
   Show answer

   The diameter of the hemisphere is $9$ cm (radius $r=4.5$ cm).

   Step-by-step solution →
6. Q326 CBSE 2017
   A solid ​metallic ​cuboid ​of dimensions $9$ ​m $\times$ $8$ m $\times$ $2$ m is melted ​and recast ​into solid cubes of edge $2$ m. Find the number of cubes so formed.
   Show answer

   The number of cubes formed is $18$.

   Step-by-step solution →
7. Q327 CBSE 2017
   Water in a canal, $5.4$ m wide and $1.8$ ​m ​deep, is flowing with a speed of $25$ km/hour. How much area can it ​irrigate ​in $40$ minutes, if $10$ ​cm of standing water is ​required for ​irrigation?
   Show answer

   Irrigable area $=1620000$ m${}^2$ $=162$ hectares

   Step-by-step solution →
8. Q328 CBSE 2017
   The $\frac{3}{4}$ th ​part of a conical vessel of internal radius $5$ cm and height $24$ cm ​is full ​of ​water. The ​water ​is emptied into a cylindrical vessel with ​internal radius $10$ cm. Find the height of water ​in cylindrical vessel.
   Show answer

   The height of water in the cylindrical vessel is $1.5$ cm.

   Step-by-step solution →
9. Q329 CBSE 2017
   A solid metallic sphere of diameter $21$ ​cm ​is melted and ​recast into a ​number of ​smaller cones, each of radius $3.5$ cm and height $3$ cm. Find the number ​of cones so formed.
   Show answer

   $126$ cones are formed.

   Step-by-step solution →
10. Q330 CBSE 2017
    Water in a canal, $5.4$ m wide and $1.8$ m deep, is ​flowing ​with ​a ​speed of $25$ km/hour. How much area can ​it irrigate ​in 40 minutes, if 10 cm of standing water is required for irrigation?
    Show answer

    The canal can irrigate $1620000$ m${}^2=162$ hectares in 40 minutes.

    Step-by-step solution →
11. Q331 CBSE 2017
    A hemisphere ​of maximum ​possible diameter is placed over a cuboidal ​block of side $7$ cm. Find ​the surface area of the ​solid ​so formed.
    Show answer

    The surface area of the solid is $332.5$ cm${}^2$.

    Step-by-step solution →
12. Q332 CBSE 2017
    Water ​is flowing ​into ​a canal, $6$ m wide ​and $1.5$ m ​deep, at the rate of $10$ km/hr. How ​much area will it irrigate in $30$ minutes, if $8$ cm of standing water is ​required for ​irrigation?
    Show answer

    The water will irrigate an area of $562500$ m${}^2$ (that is, $56.25$ hectares).

    Step-by-step solution →
13. Q333 CBSE 2017
    The dimensions of a solid ​iron cuboid ​are $4.4\text{ m}\times 2.6\text{ m}\times 1.0\text{ m}$. It is melted and recast ​into a hollow cylindrical pipe of $30$ cm inner radius and thickness $5$ ​cm. Find the length ​of the pipe.
    Show answer

    The length of the pipe is $112$ m (i.e. $11200$ cm).

    Step-by-step solution →
14. Q334 CBSE 2017
    The ​radius and ​height of a solid right ​circular cone ​are ​in the ​ratio of $5:12$. If its volume is $314{\text{cm}}^3$, find its total ​surface area. [Take $\pi =3.14$]
    Show answer

    Total surface area $=282.6{\text{cm}}^2$ (with $r=5$ cm, $h=12$ cm, $l=13$ cm).

    Step-by-step solution →
15. Q335 CBSE 2017
    From a ​solid right circular cylinder of height $2.4$ cm ​and ​radius $0.7$ ​cm, a right ​circular ​cone of same height and same radius ​is cut out. Find the total surface area of the remaining solid.
    Show answer

    Total surface area of the remaining solid $=17.6$ cm${}^2$.

    Step-by-step solution →
16. Q336 CBSE 2017
    A toy is in the form of a ​cone of radius $3.5$ cm mounted on ​a hemisphere of ​same radius on its circular face. 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 $214.5$ cm${}^2$.

    Step-by-step solution →
17. Q337 CBSE 2017
    The slant height of ​a frustum ​of ​a cone is $4$ cm and the ​perimeters of its ​circular ends ​are $18$ cm and $6$ cm. Find the ​curved surface ​area of the frustum.
    Show answer

    The curved surface area of the frustum is $48$ cm${}^2$.

    Step-by-step solution →
18. Q338 CBSE 2017
    From ​a solid ​cylinder, ​whose ​height ​is $2\times 4$ cm and diameter $1\times 4$ cm, a conical cavity of the same height and same radius is ​hollowed ​out. Find the total surface area of the remaining ​solid. (Use $\pi =\frac{22}{7}$)
    Show answer

    Total surface area of the remaining solid $=17.6$ cm${}^2$

    Step-by-step solution →
19. Q339 CBSE 2017
    The ​dimensions of a solid iron cuboid are $4.4$ ​m $\times 2.6$ m $\times 1.0$ m. It is melted and ​recast into ​a hollow ​cylindrical pipe of $30$ cm inner radius and thickness $5$ ​cm. Find the length of ​the pipe.
    Show answer

    The length of the pipe is $\ell =112$ m.

    Step-by-step solution →
20. Q340 CBSE 2017
    How ​many ​solid ​spherical bullets can be made after melting a ​solid cube of ​iron whose edge ​measures $44$ cm, each ​bullet being $4$ cm in diameter? ​[Take $\pi =\frac{22}{7}$]
    Show answer

    $2541$ spherical bullets can be made.

    Step-by-step solution →