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 10 of 20

1. Q181 CBSE 2024
   The difference between the outer and inner ​radii of ​a ​hollow right circular cylinder of ​length $14$ cm is $1$ cm. If the volume of ​the metal used in making the cylinder is $176$ ​cm${}^3$, find the outer and inner radii of the cylinder.
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   Outer radius $R=2.5$ cm and inner radius $r=1.5$ cm.

   Step-by-step solution →
2. Q182 CBSE 2024
   A vessel is in the form of a hollow ​hemisphere surmounted ​by a ​hollow cylinder of the same ​radius. 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.
   Show answer

   The inner surface area of the vessel is $572$ cm${}^2$.

   Step-by-step solution →
3. Q183 CBSE 2024
   Hemispherical depressions are scooped out from two ​opposite faces of a ​solid wooden cubical ​block of side 14 cm. If the ​diameter of ​each hemisphere is equal to the side of the cube, ​find the volume of the remaining solid wooden ​block.

   Show answer

   The volume of the remaining solid wooden block is $\frac{3920}{3}{\text{cm}}^3\approx 1306.67{\text{cm}}^3$.

   Step-by-step solution →
4. Q184 CBSE 2024
   Two ​cubes each of volume ​125 ​cm${}^3$ ​are joined ​end to end. ​Find the ​volume and ​the surface area of the resulting cuboid.
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   Volume $=250{\text{cm}}^3$; surface area $=250{\text{cm}}^2$.

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5. Q185 CBSE 2024
   A toy is in the form ​of a ​cone of ​radius 7 cm ​mounted on a hemisphere of same radius. The ​total height of ​the toy is 31 cm. Find ​the surface area of the ​toy.
   Show answer

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

   Step-by-step solution →
6. Q186 CBSE 2024
   A wooden article was made by scooping ​out a hemisphere from each ​end ​of a ​solid cylinder. If ​the height of the cylinder is 15 cm and its base is of ​radius 4.2 cm, then find ​the total surface area of ​the article.

   Show answer

   The total surface area of the article is $617.76{\text{cm}}^2$.

   Step-by-step solution →
7. Q187 CBSE 2024
   A solid is in the shape of a ​cone surmounted on a hemisphere with both their diameters being ​equal to ​7 cm and ​the height of the cone is equal ​to its radius. Find the volume ​of the ​solid.
   Show answer

   Volume of the solid $=\frac{539}{4}$ cm³ $=134.75$ cm³

   Step-by-step solution →
8. Q188 CBSE 2024
   The ​interior of a building is in the form of a cylinder of ​base radius 12 m and height $3.5$ m surmounted ​by a cone of equal ​base and ​slant height ​14 m. Find ​the internal curved surface area of the building.
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   The internal curved surface area of the building is $792{\text{m}}^2$.

   Step-by-step solution →
9. Q189 CBSE 2024
   Determine the ratio of the volume ​of a cube to ​that ​of the sphere ​which ​will ​exactly fit inside ​the cube.
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   Volume of the cube : volume of the sphere $=6:\pi$ ($\approx 21:11$ if $\pi \approx \frac{22}{7}$ is used).

   Step-by-step solution →
10. Q190 CBSE 2024
    A wooden article was made by scooping out a hemisphere ​from each end of a solid cylinder, ​as shown ​in the ​figure. If the height of the ​cylinder is $5.8$ cm ​and its base is of radius $2.1$ cm, find the total ​surface area of the ​article.

    Show answer

    The total surface area of the article is $132$ cm${}^2$.

    Step-by-step solution →
11. Q191 CBSE 2024
    A solid iron ​pole consists ​of a solid cylinder of height $200$ cm and ​base ​diameter $28$ cm, which is surmounted by another cylinder of height $50$ cm and radius $7$ cm. Find the ​mass of the pole, given that $1$ cm${}^3$ ​of iron has approximately $8$ ​g ​mass.
    Show answer

    The mass of the pole is $1047200$ g, that is $1047.2$ kg.

    Step-by-step solution →
12. Q192 CBSE 2024
    A textile industry runs in a ​shed. This shed is in ​the ​shape of a ​cuboid surmounted by a half cylinder. If the base of the ​industry is of dimensions $14\text{ m}\times 20\text{ m}$ ​and the height of the cuboidal portion is $7$ m, find the volume of air that the industry can hold. Further, suppose ​the machinery in the industry occupies a total space of $400{\text{m}}^3$. ​Then, how much space is left in the industry?

    Show answer

    The industry can hold $3500{\text{m}}^3$ of air, and the space left after the machinery is $3100{\text{m}}^3$.

    Step-by-step solution →
13. Q193 CBSE 2024
    A solid is in the form of a right circular cylinder with hemispherical ends. The ​total height of the solid ​is 58 cm ​and ​the ​diameter of the cylinder is ​28 cm. Find the total surface ​area of the solid.
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    Total surface area of the solid $=5104$ cm${}^2$.

    Step-by-step solution →
14. Q194 CBSE 2024
    The largest possible hemisphere is drilled ​out from ​a wooden cubical block of side 21 cm such that the base of the ​hemisphere is ​on one ​of ​the faces of the cube. Find :

    1. (i)the volume of wood left in ​the block,
    2. (ii)the total surface area of the ​remaining solid.

    1. (i)the volume of wood left in the block[2]
    2. (ii)the total surface area of the remaining solid[3]
    Show answer

    (i) The volume of wood left in the block is $6835.5{\text{ cm}}^3$; (ii) The total surface area of the remaining solid is $2992.5{\text{ cm}}^2$.

    Step-by-step solution →
15. Q195 CBSE 2024
    From a solid cylinder of ​height 36 cm and diameter ​14 cm, ​a conical cavity of ​radius 7 cm and height 24 cm is drilled out. Find the ​volume of the ​remaining ​solid.
    Show answer

    Volume of the remaining solid $=4312$ cm${}^3$.

    Step-by-step solution →
16. Q196 CBSE 2024
    A medicine capsule is in ​the shape of ​a cylinder with ​two ​hemispheres stuck to each of its ​ends. The length of the entire capsule ​is $14$ mm and the ​diameter of the capsule is $4$ mm, find its surface area. Also, find ​its volume.

    Show answer

    Surface area $=176$ mm${}^2$; volume $=\frac{3344}{21}\approx 159.24$ mm${}^3$.

    Step-by-step solution →
17. Q197 CBSE 2024
    A solid ​toy is in the form of a hemisphere surmounted by a right ​circular cone. Ratio of the radius ​of the cone ​to ​its slant height is 3 : 5. If the volume of the ​toy ​is $240\pi$ cm${}^3$, then find the total height of the toy.
    Show answer

    The total height of the toy is $14$ cm.

    Step-by-step solution →
18. Q198 CBSE 2024
    From a solid ​cylinder of height $8$ cm and radius $6$ cm, a conical cavity of the ​same height and same radius is carved ​out. Find ​the ​total surface area of ​the remaining solid. (Take $\pi =3.14$)
    Show answer

    The total surface area of the remaining solid is $602.88$ cm².

    Step-by-step solution →
19. Q199 CBSE 2024
    The word 'circus' has the same ​root as 'circle'. ​In ​a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical up to a height of $8$ m and conical above it. The diameter of the ​base is $28$ ​m and ​total height of tent is $18.5$ ​m. Based on the ​above, answer the following questions.

    1. (i)Find slant height of the conical part.[1]
    2. (ii)Determine the floor area of the tent.[1]
    3. (iii)(a)Find area of the cloth used for making tent.[2]
    4. (iii)(b)(OR) Find total volume of air inside an empty tent.[2]
    Show answer

    (i) Slant height $l=17.5$ m; (ii) Floor area $=616$ m${}^2$; (iii)(a) Cloth used $=1474$ m${}^2$; (iii)(b) Volume of air $=7084$ m${}^3$.

    Step-by-step solution →
20. Q200 CBSE 2024
    Tamper-proof tetra-packed milk guarantees ​both freshness and security. This milk ensures uncompromised ​quality, preserving the nutritional values ​within and making it a ​reliable choice for health-conscious individuals. $500$ mL milk is packed in a ​cuboidal container of dimensions $15$ cm $\times$ $8$ cm $\times$ $5$ cm. ​These milk packets are then packed in cuboidal cartons of ​dimensions $30$ cm $\times$ $32$ cm $\times$ $15$ ​cm. Based on the above given information, answer the following questions.

    1. (i)Find the volume of the cuboidal carton.[1]
    2. (ii)(a)Find the total surface area of a milk packet.[2]
    3. (ii)(b)How many milk packets can be filled in a carton ? (OR)[2]
    4. (iii)How much milk can the cup (as shown in the figure) hold ?[1]
    Show answer

    (i) $14400$ cm³; (ii)(a) $470$ cm²; (ii)(b) $24$ packets; (iii) $550$ cm³, that is $550$ mL.

    Step-by-step solution →