Class 10 Maths · Chapter 12

Surface Areas and Volumes

90 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 1 of 5

1. Q1 NCERT · Exercise 12.1
   2 ​cubes each ​of volume ​64 cm^3 are joined end to end. Find the ​surface ​area of the ​resulting ​cuboid.
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   Surface area of the resulting cuboid $=160$ cm².

   Step-by-step solution →
2. Q2 NCERT · Exercise 12.1
   A vessel is in the ​form of ​a ​hollow ​hemisphere mounted by a hollow cylinder. The diameter ​of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the ​inner surface ​area of ​the vessel.
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   Inner surface area $=572$ cm².

   Step-by-step solution →
3. Q3 NCERT · Exercise 12.1
   A toy ​is in the ​form of ​a cone of radius 3.5 cm mounted on a ​hemisphere ​of same radius. The total height of the toy ​is 15.5 cm. Find the total surface area of ​the toy.
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   Total surface area of the toy $=214.5$ cm².

   Step-by-step solution →
4. Q4 NCERT · Exercise 12.1
   A cubical block ​of side ​7 cm is ​surmounted by a hemisphere. ​What is ​the greatest ​diameter the hemisphere can have? Find ​the surface area ​of the solid.
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   Greatest diameter $=7$ cm; surface area $=332.5$ cm².

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5. Q5 NCERT · Exercise 12.1
   A hemispherical depression is cut out from one face ​of a cubical wooden block such that the diameter $l$ of the hemisphere ​is equal to the edge of the ​cube. Determine the surface ​area of ​the ​remaining ​solid.
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   Surface area $=6l^2+\frac{\pi l^2}{4}=\frac{l^2}{4}(24+\pi )$ square units.

   Step-by-step solution →
6. Q6 NCERT · Exercise 12.1
   A medicine capsule is in the shape of a ​cylinder with two hemispheres stuck to each of ​its ends ​(see Fig. 12.10). The length ​of the entire capsule ​is 14 mm and the diameter of the capsule is ​5 mm. ​Find its surface area.

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   Surface area $=220$ mm${}^2$.

   Step-by-step solution →
7. Q7 NCERT · Exercise 12.1
   A tent is in the shape of a cylinder surmounted by a conical top. If the height and ​diameter of ​the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the ​top is ​2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per ​m^2. ​(Note that ​the base ​of the tent will not be covered with canvas.)
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   Canvas area $=44$ m²; cost $=$ Rs $22000$.

   Step-by-step solution →
8. Q8 NCERT · Exercise 12.1
   From a ​solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, a conical cavity ​of the same ​height and same diameter is hollowed ​out. ​Find the total surface area ​of the remaining solid to the nearest ​cm${}^2$.
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   Total surface area $=17.6$ cm² $\approx 18$ cm².

   Step-by-step solution →
9. Q9 NCERT · Exercise 12.1
   A ​wooden article was made by scooping out a hemisphere from each ​end of a ​solid cylinder, ​as shown in Fig. 12.11. 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.

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   Total surface area $=374$ cm${}^2$.

   Step-by-step solution →
10. Q10 NCERT · Exercise 12.2
    A ​solid is in the shape of a ​cone ​standing ​on ​a hemisphere with both their radii being equal to $1$ cm and the height of the cone ​is equal to its radius. Find the volume of the solid in terms ​of $\pi$.
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    Volume of the solid $=\pi$ cm³ $\approx 3.14$ cm³.

    Step-by-step solution →
11. Q11 NCERT · Exercise 12.2
    Rachel, ​an engineering student, was asked to make a model shaped like a ​cylinder with two cones attached at its ​two ends by using ​a thin aluminium sheet. The diameter of ​the ​model is 3 cm and its length is ​12 cm. If each cone has a height of ​2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
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    Volume of air $=66$ cm³.

    Step-by-step solution →
12. Q12 NCERT · Exercise 12.2
    A gulab jamun ​contains sugar syrup up to about 30% of its volume. ​Find approximately ​how much ​syrup would be ​found in ​45 gulab jamuns, each ​shaped like a cylinder with two hemispherical ends, with length 5 cm and diameter 2.8 cm (see Fig. 12.15).

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    Volume of syrup $\approx 338$ cm${}^3$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 12.2
    A pen stand made of wood is in ​the ​shape of a cuboid with four conical ​depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm ​by 3.5 cm. The radius of ​each of the ​depressions is 0.5 cm ​and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 12.16).

    Show answer

    Volume of wood $\approx 523.53$ cm${}^3$ (cuboid $525$ cm${}^3$ minus four conical depressions totalling about $1.47$ cm${}^3$).

    Step-by-step solution →
14. Q14 NCERT · Exercise 12.2
    A vessel is in the form of an inverted cone. Its height is $8$ ​cm and the radius of its top, which is open, is $5$ cm. It ​is filled with water up to the brim. When lead shots, each ​of ​which is a sphere of radius $0.5$ cm are ​dropped ​into the vessel, one-fourth of the water flows out. ​Find the ​number of lead shots dropped in the vessel.
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    Number of lead shots $=100$.

    Step-by-step solution →
15. Q15 NCERT · Exercise 12.2
    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 ​g ​mass. (Use $\pi =3.14$)
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    Mass of the pole $\approx 892262.4$ g $=892.26$ kg.

    Step-by-step solution →
16. Q16 NCERT · Exercise 12.2
    A ​solid ​consisting of a right circular cone of height ​120 cm and radius 60 cm standing on a hemisphere of radius 60 ​cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the ​cylinder, if the radius of the ​cylinder ​is 60 cm and its height is ​180 cm.
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    Water left $=360000\pi$ cm³ $\approx 1131428.57$ cm³ $\approx 1.131$ m³.

    Step-by-step solution →
17. Q17 NCERT · Exercise 12.2
    A spherical glass vessel has a cylindrical neck 8 cm long, ​2 cm ​in diameter; the ​diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a ​child finds its ​volume ​to be 345 cm${}^3$. Check whether she ​is correct, taking the above as the inside measurements, and $\pi =3.14$.
    Show answer

    The vessel's capacity is about $346.51$ cm³, so the child is not correct ($345$ cm³ is too low).

    Step-by-step solution →
18. Q18 Exemplar · Exercise 12.1
    A cylindrical ​pencil ​sharpened ​at ​one ​edge ​is the combination of

    1. (a)a cone and a cylinder
    2. (b)frustum of a cone and a cylinder
    3. (c)a hemisphere and a cylinder
    4. (d)two cylinders.
    Show answer

    (a) a cone and a cylinder

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19. Q19 Exemplar · Exercise 12.1
    A surahi is the combination of

    1. (a)a sphere and a cylinder
    2. (b)a hemisphere and a cylinder
    3. (c)two hemispheres
    4. (d)a cylinder and a cone
    Show answer

    (a) a sphere and a cylinder

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20. Q20 Exemplar · Exercise 12.1
    A ​plumbline ​(sahul) ​is ​the ​combination of ​(see ​Fig. 12.2)

    1. (a)a cone and a cylinder
    2. (b)a hemisphere and a cone
    3. (c)frustum of a cone and a cylinder
    4. (d)sphere and cylinder
    Show answer

    (b) a hemisphere and a cone

    Step-by-step solution →