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 12 of 20

1. Q221 CBSE 2023
   A tent is in the ​shape of a right circular cylinder up to a height of 3 m and then a right circular ​cone, with a maximum height of 13.5 m above the ground. Calculate ​the ​cost of painting the inner side ​of the tent at the rate ​of Rs 2 ​per square metre, if the radius of the base is 14 m.
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   Total curved surface $=1034$ m${}^2$; cost of painting $=$ Rs $2068$.

   Step-by-step solution →
2. Q222 CBSE 2023
   A solid wooden toy is in the shape of a right circular ​cone mounted on a hemisphere of ​same radius. If the radius of the hemisphere is 4.2 cm and the ​total height of the ​toy is 10.2 cm, ​find the volume of the ​wooden toy. ​Also, ​find the total surface area of the toy.
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   Volume $\approx 266.11$ cm${}^3$; total surface area $\approx 207.5$ cm${}^2$.

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3. Q223 CBSE 2023
   A vessel is in the form of ​a hemispherical bowl surmounted by a hollow ​cylinder of same diameter. The diameter of ​the hemispherical bowl is $14$ cm ​and ​the total height of the vessel is $13$ cm. ​Find the inner surface ​area of the ​vessel. Also, find the volume of the vessel.
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   Inner surface area $=572$ cm${}^2$; volume $\approx 1642.67$ cm${}^3$.

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4. Q224 CBSE 2023
   A solid is ​in the shape of a right-circular ​cone surmounted ​on ​a hemisphere, the ​radius of each of ​them being 7 cm and the height of the cone is equal to ​its diameter. Find the volume of the solid.
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   $V=\frac{4312}{3}\approx 1437.33$ cm${}^3$

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5. Q225 CBSE 2023
   An ice-cream ​filled ​cone having radius $5$ cm and height $10$ cm ​is as ​shown in ​the figure. ​Find ​the volume of the ice-cream in $7$ ​such cones.

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   Total volume $=\frac{11000}{3}\approx 3666.67$ cm${}^3$

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6. Q226 CBSE 2023
   A student was ​asked to make a model ​shaped like a cylinder with two cones attached to its ends by using a thin aluminium ​sheet. The diameter of the model is 3 cm and its ​total length is 12 ​cm. If each cone has ​a height of 2 cm, find ​the volume of air ​contained in the model.
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   $V=21\pi =66{\text{cm}}^3$

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7. Q227 CBSE 2023
   From a solid cone, ​whose height is 16 ​cm and ​radius of ​base is 12 cm, a right ​circular cylindrical cavity ​of height 3 cm and radius 4 cm ​is hollowed out such that bases of cone and cylinder form concentric circles. Find the volume of the remaining solid.
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   $\frac{15840}{7}\approx 2262.86$ cm${}^3$

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8. Q228 CBSE 2023
   A solid toy ​is in the form ​of a hemisphere surmounted by a right circular cone, the ​diameter ​of both is 14 cm ​and the height of ​cone is 24 cm. Find the total surface area and the volume of the ​toy.
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   TSA $=858{\text{cm}}^2$; Volume $=\frac{5852}{3}\approx 1950.67{\text{cm}}^3$.

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9. Q229 CBSE 2023
   A hemispherical depression is cut off from one face of ​a cubical wooden block ​such that the diameter 14 cm of ​the hemisphere is equal ​to the ​edge ​of the cube. Determine the surface area of the remaining solid.
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   $1330$ cm${}^2$

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10. Q230 CBSE 2023
    The boilers are used in thermal power plants to store water ​and then used to produce steam. One such ​boiler consists of a cylindrical part ​in ​middle and two hemispherical parts at its both ends. Length of the cylindrical part is $7$ m and radius ​of cylindrical part is $\frac{7}{2}$ m. Find the total surface area ​and the volume of the boiler. Also, find the ratio of the volume of cylindrical part ​to ​the volume of one hemispherical part.

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    TSA $=308$ m${}^2$; Volume $=\frac{2695}{6}\approx 449.17$ m${}^3$; ratio of cylindrical volume to one hemispherical volume $=3:1$.

    Step-by-step solution →
11. Q231 CBSE 2023
    Case ​Study - 1. A golf ball is spherical with ​about $300-500$ ​dimples that help increase its velocity while in play. Golf ​balls ​are traditionally white but ​available in colours ​also. In the given figure, a golf ball has diameter $4.2$ cm and the surface has $315$ dimples (hemi-spherical) of radius $2$ ​mm. Based on the above, answer the following questions :

    1. (i)Find the surface area of one such dimple.[1]
    2. (ii)Find the volume of the material dug out to make one dimple.[1]
    3. (iii) (a)Find the total surface area exposed to the surroundings.[2]
    4. (iii) (b)Find the volume of the golf ball.[2]
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    (i) $\approx 0.251$ cm${}^2$; (ii) $\approx 0.0168$ cm${}^3$; (iii)(a) $95.04$ cm${}^2$; (iii)(b) $33.528\approx 33.53$ cm${}^3$

    Step-by-step solution →
12. Q232 CBSE 2023
    The great Stupa at Sanchi ​is one ​of the oldest stone structures in India ​which was originally ​made by ​Emperor Ashoka. It is basically a big ​hemispherical dome with a cuboidal ​structure mounted on it. Based on the above, answer the following questions:

    1. iWhat is the volume of the hemispherical dome, if its height is $21$ m? (use $\pi =\frac{22}{7}$)
    2. iiWhat is the area of plastic cloth required to cover the hemispherical dome, if the radius of its base is $14$ m?
    3. iii-aIf the dimensions of the cuboidal top are $8\text{ m}\times 6\text{ m}\times 4\text{ m}$, then what is the surface area of this cuboidal top?
    4. iii-bOR What is the volume of the cuboidal top of the dimensions given in part (iii)?
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    (i) $19404$ m${}^3$; (ii) $1232$ m${}^2$; (iii)(a) $208$ m${}^2$; (iii)(b) $192$ m${}^3$.

    Step-by-step solution →
13. Q233 CBSE 2023
    Singing ​bowls (hemispherical ​in shape) are commonly used in sound healing practices. Mallet (cylindrical in shape) is used to strike the bowl in a sequence to produce sound and vibration. One such bowl is shown ​here ​whose dimensions are : Hemispherical bowl has outer radius 6 cm and inner radius 5 cm. Mallet has height of 10 cm and ​radius ​2 cm. Based on the above, answer the following ​questions :

    1. (i)What is the volume of the material used in making the mallet ?[1]
    2. (ii)The bowl is to be polished from inside. Find the inner surface area of the bowl.[1]
    3. (iii)(a)Find the volume of metal used to make the bowl.[2]
    4. (iii)(b) ORFind total surface area of the mallet. $(\text{Use }\pi =3.14)$[2]
    Show answer

    (i) $125.6$ cm${}^3$; (ii) $157$ cm${}^2$; (iii)(a) $\approx 190.49$ cm${}^3$; (iii)(b) $150.72$ cm${}^2$.

    Step-by-step solution →
14. Q234 CBSE 2023
    In a coffee shop, coffee is served in two types ​of cups. One is cylindrical in ​shape with diameter $7$ cm and height $14$ ​cm and the other ​is hemispherical ​with diameter $21$ ​cm. Based on ​the above, answer the following questions:

    1. (i)Find the area of the base of the cylindrical cup.[1]
    2. (ii)(a)What is the capacity of the hemispherical cup?[2]
    3. (ii)(b)Find the capacity of the cylindrical cup.[2]
    4. (iii)What is the curved surface area of the cylindrical cup?[1]
    Show answer

    (i) $38.5$ cm${}^2$; (ii)(a) $2425.5$ cm${}^3$; (ii)(b) $539$ cm${}^3$; (iii) $308$ cm${}^2$.

    Step-by-step solution →
15. Q235 CBSE 2023
    A wooden toy is shown in ​the picture. This ​is a cuboidal wooden block ​of dimensions $14$ cm $\times$ $17$ cm $\times$ $4$ cm. On its top there ​are ​seven cylindrical hollows ​for bees to fit in. Each cylindrical hollow is of height $3$ ​cm and radius $2$ ​cm.

    1. (i)Find the volume of wood carved out to make one cylindrical hollow.[1]
    2. (ii)Find the lateral surface area of the cuboid to paint it with green colour.[1]
    3. (iii)(a)Find the volume of wood in the remaining cuboid after carving out seven cylindrical hollows.[2]
    4. (iii)(b)OR Find the surface area of the top surface of the cuboid to be painted yellow.[2]
    Show answer

    (i) $\frac{264}{7}\approx 37.71$ cm${}^3$; (ii) $248$ cm${}^2$; (iii a) $688$ cm${}^3$; (iii b) $150$ cm${}^2$.

    Step-by-step solution →
16. Q236 CBSE 2023
    For the Kumbh Mela, Uttar Pradesh Government prescribed the following for ​the contractors to pitch the tents. Each tent must be of cylindrical base of radius $21$ m and height $5$ m, ​surmounted by a conical part of height $20$ m. ​The cylindrical ​part must have a white coloured ​thick fabric costing Rs $60$ per square meter, while the conical part must have PVC coated blue fabric costing Rs $70$ per square meter. Based on the above information, answer the following questions:

    1. (a)​How much blue PVC (in sq.m) is required and what ​will be ​its total cost?
    2. (b)How much white fabric (in sq.m) is required and what will be its total cost?

    1. aHow much blue PVC (in sq.m) is required for the conical part and its total cost?[2]
    2. bHow much white fabric (in sq.m) is required for the cylindrical part and its total cost?[2]
    Show answer

    Blue PVC $=1914$ m${}^2$ (Rs $133980$); white fabric $=660$ m${}^2$ (Rs $39600$)

    Step-by-step solution →
17. Q237 CBSE 2022
    A ​solid ​metallic sphere of radius 3 ​cm is ​melted and recast into the shape of a solid ​cylinder ​of radius 2 ​cm. Find ​the height of the cylinder.
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    Height of the cylinder $h=9$ cm.

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18. Q238 CBSE 2022
    A ​solid metallic ​sphere of radius $10.5$ 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.
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    $N=126$ cones

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19. Q239 CBSE 2022
    A ​solid piece ​of metal in the form of ​a cuboid of dimensions $11\text{ cm}\times 7\text{ cm}\times 7\text{ cm}$ ​is ​melted ​to form $n$ number of solid spheres ​of radii $\frac{7}{2}$ cm each. Find the value of $n$.
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    $n=3$ spheres

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20. Q240 CBSE 2022
    $3$ cubes ​each ​of $8$ cm edge ​are joined end to end. ​Find the ​total ​surface area ​of the cuboid so formed.
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    Total surface area $=896$ cm${}^2$.

    Step-by-step solution →