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 16 of 20

1. Q301 CBSE 2019
   A farmer ​connects ​a pipe of internal diameter $20$ cm from a canal into a ​cylindrical tank in his field ​which is $10$ m in diameter ​and $2$ m ​deep. If ​water flows ​through the pipe at the rate of $3$ km/hr, in how much time will the tank be filled?
   Show answer

   The tank is filled in $\frac{5}{3}$ hours $=100$ minutes.

   Step-by-step solution →
2. Q302 CBSE 2019
   Water in a canal, $6$ m ​wide and $1.5$ ​m deep, ​is ​flowing ​with a speed of $10$ km/h. How much area will ​it irrigate ​in $30$ minutes if $8$ ​cm of standing water is needed?
   Show answer

   Area irrigated $=562500{\text{ m}}^2$ (i.e. $56.25$ hectares)

   Step-by-step solution →
3. Q303 CBSE 2019
   Water is flowing at the rate ​of $5$ km/hour through a pipe of diameter $14$ cm into a tank with rectangular base ​which ​is $50$ m ​long ​and $44$ m wide. ​Find the time in which the level ​of water in the tank rises by $7$ ​cm. (Use $\pi =\frac{22}{7}$)
   Show answer

   The water level rises by $7$ cm in $2$ hours.

   Step-by-step solution →
4. Q304 CBSE 2019
   A field is in ​the form ​of a rectangle of length $20$ ​m and width $14$ ​m. A $10$ m deep well of diameter $7$ m is dug in one corner of the field and the earth taken out of the well is spread evenly over ​the remaining part of the field. Find the ​rise in the ​level of the field. (Use $\pi =\frac{22}{7}$)
   Show answer

   The level of the field rises by $\frac{385}{241.5}=\frac{110}{69}\approx 1.59$ m.

   Step-by-step solution →
5. Q305 CBSE 2019
   Water in a canal, $6$ m wide ​and $1.5$ m ​deep, is flowing with a speed of $10$ km/hour. ​How much ​area will ​it irrigate ​in $30$ ​minutes, if $8$ cm of standing water is needed?
   Show answer

   $A=562500{\text{m}}^2$ (i.e. $56.25$ hectares)

   Step-by-step solution →
6. Q306 CBSE 2019
   A juice seller was serving his customers using glasses as shown in Figure 3. The inner ​diameter of the ​cylindrical glass was $5$ ​cm but bottom of the glass ​had ​a hemispherical raised portion which ​reduced the capacity of the glass. If the height of a glass was $10$ cm, find the apparent and actual capacity of the glass. ​(Use $\pi =3.14$)

   Show answer

   Apparent capacity $=196.25{\text{cm}}^3$; actual capacity $\approx 163.54{\text{cm}}^3$.

   Step-by-step solution →
7. Q307 CBSE 2019
   A girl ​empties a cylindrical bucket full of ​sand, of base radius $18$ cm and height $32$ ​cm on the floor to form a conical heap of sand. If the height ​of this ​conical ​heap is $24$ cm, then find its slant ​height ​correct to one place of decimal.
   Show answer

   Slant height $l=12\sqrt{13}\approx 43.3$ cm.

   Step-by-step solution →
8. Q308 CBSE 2019
   A ​solid ​iron pole consists of a cylinder of height $220$ cm and base diameter $24$ ​cm, which is surmounted by ​another cylinder of height $60$ cm and radius $8$ ​cm. Find the mass ​of the pole, given that $1$ cm${}^3$ of iron has ​approximately $8$ gm mass. ​(Use $\pi =3.14$)
   Show answer

   Mass of the pole $=892262\cdot 4$ g $\approx 892.26$ kg.

   Step-by-step solution →
9. Q309 CBSE 2019
   In Figure 3, a decorative ​block ​is shown which is made of ​two solids, a ​cube and a hemisphere. The base of the block is a cube with edge $6$ cm and ​the hemisphere ​fixed on the top has a diameter of $4.2$ cm. Find

   1. (a)the total surface area of the block.
   2. (b)the volume of the block formed. (Take $\pi =\frac{22}{7}$)

   1. athe total surface area of the block.[2]
   2. bthe volume of the block formed. (Take $\pi =\frac{22}{7}$)[2]
   Show answer

   (a) Total surface area $=229.86{\text{ cm}}^2$; (b) Volume $=235.404{\text{ cm}}^3$

   Step-by-step solution →
10. Q310 CBSE 2019
    A bucket open ​at the top is in ​the form of a ​frustum of ​a cone with ​a capacity of $12308.8$ cm${}^3$. The radii of the top and bottom circular ends are $20$ cm ​and $12$ cm ​respectively. Find the height of the bucket and the area of metal ​sheet used in making the bucket. (Use $\pi =3.14$)
    Show answer

    Height $=15$ cm; area of metal sheet $=2160.32$ cm${}^2$.

    Step-by-step solution →
11. Q311 CBSE 2019
    A bucket open at the top is in the form of a frustum of a cone with ​a capacity of $12308.8$ cm${}^3$. The ​radii of the top and ​bottom of circular ​ends ​of the bucket are $20$ cm ​and $12$ cm respectively. Find the height of the bucket and also the area of ​the metal sheet used ​in making it. (Use $\pi =3.14$)
    Show answer

    Height $=15$ cm; area of metal sheet $=2160.32$ cm${}^2$.

    Step-by-step solution →
12. Q312 CBSE 2019
    An open metallic bucket is in the shape of a ​frustum of a cone. If the diameters of the ​two circular ends of the bucket ​are $45$ cm and $25$ cm and the vertical ​height ​of the bucket is $24$ cm, find the area of the metallic sheet used to make the ​bucket. Also find the volume of the water it can hold. ​(Use $\pi =\frac{22}{7}$)

    Show answer

    Metallic sheet $\approx 3351.07{\text{cm}}^2$ and volume $\approx 23728.57{\text{cm}}^3$ ($\approx 23.73$ litres).

    Step-by-step solution →
13. Q313 CBSE 2019
    A container is in the form of a frustum of a cone of height $16$ ​cm ​and the radii of its ​lower and upper ends are $8$ cm and $20$ cm respectively. Find the cost of ​milk ​which can completely fill the container at the rate ​of ₹ $42$ per litre. (Use $\pi =\frac{22}{7}$)
    Show answer

    The container holds about $10.459$ litres, so the cost of the milk is approximately ₹$439.30$.

    Step-by-step solution →
14. Q314 CBSE 2019
    A container opened ​at the top and made up ​of a metal ​sheet, is ​in the form of a frustum ​of a cone of height $16$ cm with radii of its lower and ​upper ends as $8$ cm and $20$ cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ $50$ per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ $10$ per $100$ cm${}^2$. ​(Take $\pi =3.14$)
    Show answer

    Cost of milk $\approx$ ₹ $522.50$ and cost of metal sheet $\approx$ ₹ $195.94$.

    Step-by-step solution →
15. Q315 CBSE 2018
    A wooden article was made by scooping out a hemisphere ​from ​each end of a solid cylinder, as ​shown in Fig. 2. If the height of ​the ​cylinder is ​10 cm and its base is of ​radius 3.5 cm, find the total surface area of the ​article.

    Show answer

    The total surface area of the article is $374$ cm².

    Step-by-step solution →
16. Q316 CBSE 2018
    A heap of rice is in the form of a cone of ​base diameter 24 m and height ​3.5 m. Find the volume of the rice. How much canvas ​cloth is ​required to just ​cover the ​heap?
    Show answer

    Volume of rice $=528{\text{m}}^3$; canvas required $=\frac{3300}{7}\approx 471.4{\text{m}}^2$.

    Step-by-step solution →
17. Q317 CBSE 2018
    A ​wooden article ​was made by scooping out a ​hemisphere from each end of a solid cylinder, as shown in Fig. ​2. If the height of the ​cylinder is $10$ cm ​and ​its base is of radius $3.5$ cm, find the total surface ​area of the article.

    Show answer

    Total surface area $=374{\text{ cm}}^2$

    Step-by-step solution →
18. Q318 CBSE 2018
    A ​sphere of diameter $12$ cm is dropped in a right circular cylindrical vessel, partly filled with water. ​If ​the ​sphere is completely submerged in ​water, the water level in the vessel rises ​by $3\frac{5}{9}$ cm. Find the diameter ​of the ​cylindrical vessel.
    Show answer

    Diameter of the cylindrical vessel $=18$ cm.

    Step-by-step solution →
19. Q319 CBSE 2018
    A ​wooden article was made by scooping out a hemisphere from each end ​of a solid cylinder, as shown in Fig. 3. If the height ​of the cylinder is $10$ cm and its base is of ​radius $3.5$ cm. Find ​the total ​surface ​area of the article.

    Show answer

    The total surface area of the article is $374$ cm².

    Step-by-step solution →
20. Q320 CBSE 2018
    A heap of ​rice is in the form of a cone ​of base ​diameter $24$ m and height $3.5$ m. ​Find the volume of the rice. How ​much canvas cloth is required to just cover the heap ​?
    Show answer

    Volume of rice $=528$ m³; canvas required $=\frac{3300}{7}\approx 471.43$ m².

    Step-by-step solution →