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 14 of 20

1. Q261 CBSE 2022
   John planned a birthday party for his younger sister ​with his friends. They decided to make some birthday caps by themselves and ​to buy a ​cake from a bakery ​shop. For these two items, ​they decided the following ​dimensions : Cake : Cylindrical shape with ​diameter 24 cm and ​height 14 cm. Cap : Conical shape with base circumference 44 cm and height 24 cm.

   1. (a)How many square cm of paper would be used to make 4 such caps ?[2]
   2. (b)The bakery shop sells cakes by weight ($0.5$ kg, 1 kg, $1.5$ kg, etc.). To have the required dimensions, how much cake should they order, if 650 cm${}^3$ equals 100 g of cake ?[2]
   Show answer

   (a) $2200$ cm${}^2$ of paper for 4 caps. (b) Cake volume $\approx 6336$ cm${}^3\approx 974.8$ g, so they should order a 1 kg cake.

   Step-by-step solution →
2. Q262 CBSE 2022
   A solid cuboidal toy is ​made of wood. It has five cone shaped cavities to hold ​toy ​carrots. ​The dimensions of the toy are ​cuboid $10$ cm $\times$ $10$ cm $\times$ $8$ ​cm. Each cone carved ​out has Radius $=2.1$ cm and Height $=6$ cm.

   1. 1Find the volume of wood carved out to make five conical cavities.[2]
   2. 2Find the volume of the wood in the final product.[2]
   Show answer

   Wood carved out (five cones) $=138.6$ cm${}^3$; wood in the final product $=661.4$ cm${}^3$.

   Step-by-step solution →
3. Q263 CBSE 2022
   Case Study - 2 A 'circus' is a company ​of performers who put on shows of acrobats, clowns etc. to entertain people, started around 250 years ​back, in open ​fields, now generally performed ​in tents. ​One such 'Circus Tent' is shown below. The tent is in the shape of a ​cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 9 m and 30 m respectively, and the height of ​the conical part is 8 m with same diameter as that of the cylindrical ​part, then find:

   1. 1The area of the canvas used in making the tent.[2]
   2. 2The cost of the canvas bought for the tent at the rate of Rs 200 per sq m, if 30 sq m canvas was wasted during stitching.[2]
   Show answer

   Part (1): canvas area $=1650$ m${}^2$. Part (2): cost $=$ Rs 3,36,000.

   Step-by-step solution →
4. Q264 CBSE 2022
   A ​company deals in casting and moulding of metal on orders received from ​its clients. ​In one such order, ​company is supposed to make $50$ toys in the form of a hemisphere surmounted by a right circular ​cone ​of the same base radius as that of hemisphere. If the ​radius of the base of the cone is $21$ cm and height is $28$ cm.

   1. aFind the volume of 50 toys.[2]
   2. bFind the ratio of the volume of hemisphere to the volume of cone.[2]
   Show answer

   Volume of 50 toys $=1,617,000$ cm${}^3$; ratio hemisphere : cone $=3:2$

   Step-by-step solution →
5. Q265 CBSE 2020
   The ​radius ​of a sphere (in cm) ​whose ​volume ​is $12\pi$ ​cm${}^3$, is

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

   (c) $3^{2/3}$

   Step-by-step solution →
6. Q266 CBSE 2020
   Total ​surface ​area ​of ​a solid ​hemisphere is

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

   (a) $3\pi r^2$

   Step-by-step solution →
7. Q267 CBSE 2020
   The diameter ​of a ​sphere ​of volume $1437\frac{1}{3}$ ​cu. cm is ​________ ​cm. (Use $\pi =\frac{22}{7}$)
   Show answer

   The diameter is $14$ cm.

   Step-by-step solution →
8. Q268 CBSE 2020
   If the radius ​of ​a solid right circular ​cylinder ​is $7$ cm and its height ​is $10$ ​cm, then its ​total ​surface area is ____ ${\text{cm}}^2$.
   Show answer

   Total surface area $=748{\text{ cm}}^2$.

   Step-by-step solution →
9. Q269 CBSE 2020
   A spherical ​metal ball ​of radius $8$ cm ​is ​melted to make $8$ smaller ​identical balls. The radius of each new ball ​is __________ cm.
   Show answer

   The radius of each new ball is $4$ cm.

   Step-by-step solution →
10. Q270 CBSE 2020
    Two right ​circular cones have their heights in the ratio $1:3$ and ​radii ​in the ​ratio $3:1$, what is the ratio ​of ​their ​volumes?
    Show answer

    $V_1:V_2=3:1$

    Step-by-step solution →
11. Q271 CBSE 2020
    Two ​cones have their heights ​in the ratio $1:3$ ​and ​radii in ​the ratio $3:1$. ​What ​is the ratio of ​their volumes?
    Show answer

    Ratio of volumes $=3:1$

    Step-by-step solution →
12. Q272 CBSE 2020
    A cylindrical bucket, ​32 ​cm ​high and with radius of base 14 ​cm, is filled completely with ​sand. Find the ​volume of ​the sand. (Use $\pi =\frac{22}{7}$)
    Show answer

    $V=19712{\text{cm}}^3$.

    Step-by-step solution →
13. Q273 CBSE 2020
    Read the following passage and answer the ​questions given at the end: Students of Class XII presented a gift to their school ​in the form ​of ​an ​electric lamp in the shape of a glass ​hemispherical base surmounted by a metallic cylindrical top of same radius $21$ ​cm and height $3.5$ cm. The top was silver coated and the ​glass surface was painted red.

    1. (i)What is the cost of silver coating the top at the rate of ₹ 5 per 100 cm${}^2$?[2]
    2. (ii)What is the surface area of glass to be painted red?[2]
    Show answer

    (i) Cost of silver coating $=$ ₹ $92.40$ (for $1848$ cm${}^2$). (ii) Red-painted glass surface area $=2772$ cm${}^2$.

    Step-by-step solution →
14. Q274 CBSE 2020
    The volume ​of a ​right ​circular ​cylinder ​with its height equal to ​the radius is $25\frac{1}{7}$ cm${}^3$. Find ​the ​height of the cylinder. $\left(\text{Use }\pi =\frac{22}{7}\right)$
    Show answer

    Height of the cylinder $=2$ cm.

    Step-by-step solution →
15. Q275 CBSE 2020
    $100$ jugs of equal volume full ​of water ​are emptied in a conical flask and the level of water in ​the ​flask is $75$ ​cm. If each jug ​contains $3850$ ​cm${}^3$ ​of water, then find the diameter of the level of water in the flask.
    Show answer

    The diameter of the water level in the flask is $140$ cm.

    Step-by-step solution →
16. Q276 CBSE 2020
    In ​Figure-6, a tent is in the shape ​of ​a cylinder surmounted by a conical top. The cylindrical ​part ​is $2.1$ m high ​and conical ​part has slant height $2.8$ m. Both the parts have ​same radius $2$ m. Find the area of the canvas used to make the tent. (Use $\pi =\frac{22}{7}$)

    Show answer

    Area of canvas $=44$ m${}^2$.

    Step-by-step solution →
17. Q277 CBSE 2020
    Three ​cubes each of ​volume $216$ cm${}^3$ are joined ​end to end to form a ​cuboid. Find ​the ​total surface area of resulting ​cuboid.
    Show answer

    Total surface area $=504$ cm${}^2$.

    Step-by-step solution →
18. Q278 CBSE 2020
    $2$ cubes, each of volume $125$ ​cm${}^3$, are ​joined end ​to end. ​Find the ​surface area of the ​resulting ​cuboid.
    Show answer

    The surface area of the resulting cuboid is $250$ cm${}^2$.

    Step-by-step solution →
19. Q279 CBSE 2020
    A solid metallic ​cuboid of dimension $24\text{ cm}\times 11\text{ cm}\times 7\text{ cm}$ is melted and recast into solid cones of ​base radius $3.5$ ​cm ​and ​height $6$ cm. Find the number of ​cones so ​formed.
    Show answer

    Number of cones $=24$

    Step-by-step solution →
20. Q280 CBSE 2020
    A cone of base ​radius $4$ cm is divided into two ​parts by drawing a plane through the mid-point of its ​height and parallel to its base. ​Compare the volume of ​the ​two parts.
    Show answer

    The volume of the small upper cone to the lower frustum is $1:7$.

    Step-by-step solution →