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 8 of 20

1. Q141 CBSE 2025
   A toy is in the form of a cone ​surmounted on a hemisphere. The ​cone and hemisphere have the same radii. The height of the conical part of the toy is equal ​to ​the diameter of its base. If ​the radius of the conical part is 5 cm, find the ​volume of the toy.
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   Volume of the toy $=\frac{11000}{21}$ cm${}^3$ $\approx 523.81$ cm${}^3$ (taking $\pi =\frac{22}{7}$).

   Step-by-step solution →
2. Q142 CBSE 2025
   From ​one of ​the faces ​of a solid wooden cube of side $14$ ​cm, maximum number of hemispheres of diameter $1.4$ ​cm are scooped out. Find the total number of ​hemispheres that can be ​scooped out. Also, find the total ​surface area of the remaining solid.
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   $100$ hemispheres can be scooped out, and the total surface area of the remaining solid is $1330$ cm${}^2$.

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3. Q143 CBSE 2025
   A hemispherical bowl of internal diameter $42$ cm contains a liquid. ​This liquid ​is ​to be filled in cylindrical bottles of radius $3$ cm ​and height $8$ ​cm. How many bottles ​are required ​to empty the ​bowl?
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   $86$ bottles are required: the liquid fills $85.75$ bottles, so $85$ bottles are filled completely and the $86^{\text{th}}$ bottle is three-quarters full.

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4. Q144 CBSE 2025
   A $16$ ​m deep well with diameter $3.5$ m is dug ​up and the earth ​from it ​is ​spread evenly to ​form a platform $27.5$ ​m $\times$ $7$ m. ​Find the height of the platform.
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   The height of the platform is $0.8$ m, that is, $80$ cm.

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5. Q145 CBSE 2025
   From a ​solid cylinder of ​height $24$ cm and radius $5$ cm, two ​cones of height $12$ cm and radius $5$ cm are hollowed out. Find ​the ​volume and surface area ​of ​the remaining solid.
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   The volume of the remaining solid is $\frac{8800}{7}{\text{cm}}^3\approx 1257.14{\text{cm}}^3$ and its surface area is $\frac{8140}{7}{\text{cm}}^2\approx 1162.86{\text{cm}}^2$.

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6. Q146 CBSE 2025
   A cubical block is surmounted by a hemisphere of radius 3.5 cm. What is the ​smallest possible length of the ​edge of the ​cube so that the hemisphere ​can totally ​lie on the cube? Find the total ​surface area of the solid so formed.
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   The smallest edge of the cube is $7$ cm, and the total surface area of the solid is $332.5$ cm${}^2$ $\left(=\frac{665}{2}{\text{cm}}^2\right)$.

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7. Q147 CBSE 2025
   A tent is of the ​shape ​of a right ​circular cylinder up to a height ​of $3$ metres surmounted by a right circular cone of ​same radius such that the total height of the tent is $13.5$ metres above the ground. Calculate the cost of painting the inner side ​of the tent at the rate of $\text{₹}2$ per ​square metre, if the radius of ​the base is $14$ metres.
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   The area to be painted is $1034$ m${}^2$, so the cost of painting the inner side of the tent is ₹$2068$.

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8. Q148 CBSE 2025
   A ​solid is composed of a cylinder with hemispherical ​ends. If the total height ​of the solid is $16.2$ ​cm and the ​diameter of ​the cylinder is $4.2$ cm, find the volume and total surface ​area of the ​solid. $\left[\pi =\frac{22}{7}\right]$
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   Volume of the solid $=205.128$ cm${}^3$; total surface area of the solid $=213.84$ cm${}^2$.

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9. Q149 CBSE 2025
   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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   The number of lead shots dropped in the vessel is $100$.

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10. Q150 CBSE 2025
    A tent is in the shape of a cylinder surmounted by a conical top of same radius. 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 $m^2$.
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    Area of canvas $=44{\text{m}}^2$; cost of the canvas $=$ ₹ $22000$.

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11. Q151 CBSE 2025
    From ​a solid cylinder of height $2.4$ cm ​and radius $0.7$ cm, ​a conical ​cavity of the same height and same radius is hollowed out. Find the ​volume and ​total surface area of ​the remaining solid.
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    Volume of the remaining solid $=2.464$ cm${}^3$; total surface area $=17.6$ cm${}^2$.

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12. Q152 CBSE 2025
    A carpenter is making a wooden toy (lattu) which is conical in shape ​and ​surmounted by a hemisphere. The ratio of ​the height of the ​hemisphere and the cone is 3:4. If the radius of the cone and the hemisphere is $2.1$ cm, find the volume of wood required to make this ​toy. ​Also, find the area ​to be painted after making the toy.
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    Volume of wood required $=32.34$ cm${}^3$; area to be painted $=50.82$ cm${}^2$.

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13. Q153 CBSE 2025
    Playing in a ​ball pool is ​good entertainment ​for kids. Suhana bought $600$ new balls of diameter $7$ ​cm to ​fill in the pool for her kids. The cuboidal box containing $600$ ​balls has dimensions $42\text{ cm}\times 91\text{ cm}\times 50\text{ cm}$ $(l\times b\times h)$. Based on above ​information, answer the following questions :

    1. (i)Find the volume of one ball.[1]
    2. (ii)10 balls are painted with neon colours. Determine the area of painted surface.[1]
    3. (iii)(a)Find the volume of empty space in the box.[2]
    4. (iii)(b)OR : The lowermost layer of the balls covers the base of the box edge to edge when balls are placed evenly adjacent to each other. (A) How much area is covered by one ball? (B) How many balls are there in lowermost layer?[2]
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    (i) Volume of one ball $=\frac{539}{3}{\text{cm}}^3\approx 179.67{\text{cm}}^3$; (ii) Area of painted surface $=1540{\text{cm}}^2$; (iii)(a) Volume of empty space $=83300{\text{cm}}^3$ OR (iii)(b) (A) Area covered by one ball $=49{\text{cm}}^2$, (B) Number of balls in the lowermost layer $=78$.

    Step-by-step solution →
14. Q154 CBSE 2025
    To make the teaching-learning ​process easier, creative and innovative, ​a teacher brings clay in ​the classroom to teach the topic of mensuration. She ​forms a cylinder of radius $2.1$ cm and height $5$ cm with the clay and puts a hemisphere of same radius on ​its top ​in such a way that the ​base of hemisphere covers the top of cylinder. Using the ​above information, and $\pi =\frac{22}{7}$, find the following.

    1. (a)The volume of cylinder so formed.[1]
    2. (b)The volume of hemispherical part.[1]
    3. (c)(i)The surface area of the complete solid.[2]
    4. (c)(ii)OR — The surface area of the cylindrical part, if hemisphere is not put on it.[2]
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    (a) The volume of the cylinder is $69.3$ cm${}^3$; (b) The volume of the hemispherical part is $19.404$ cm${}^3$; (c)(i) The surface area of the complete solid is $107.58$ cm${}^2$; (c)(ii) The surface area of the cylinder without the hemisphere is $93.72$ cm${}^2$.

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15. Q155 CBSE 2025
    A hemispherical bowl is ​packed in a cuboidal ​box. The bowl just fits ​in ​the box. Inner radius of the bowl is $10$ cm. ​Outer radius of the bowl is $10.5$ ​cm. Based on the above, answer the ​following ​questions.

    1. iFind the dimensions of the cuboidal box.[1]
    2. iiFind the total outer surface area of the box.[1]
    3. iii(a)Find the difference between the capacity of the bowl and the volume of the box. (use $\pi =3.14$)[2]
    4. iii(b)The inner surface of the bowl and the thickness is to be painted. Find the area to be painted.[2]
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    (i) Length $21$ cm, breadth $21$ cm, height $10.5$ cm; (ii) Total outer surface area $=1764$ cm²; (iii)(a) Difference $=\frac{15223}{6}\approx 2537.17$ cm³; (iii)(b) Area to be painted $=210.25\pi$ cm², which is $\frac{9251}{14}\approx 660.79$ cm² with $\pi =\frac{22}{7}$ (or $\approx 660.19$ cm² with $\pi =3.14$).

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16. Q156 CBSE 2025
    A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood - two small ones on the ends ​and one larger ​in the centre to create a perfect ​tool. The baker ​loved the rolling ​pin, as it rolled out ​the smoothest dough for breads and pastries. The ​length of the bigger ​cylindrical part is $12$ cm and diameter is $7$ cm and the length of each smaller cylindrical part is $5$ cm and diameter is $2.1$ cm.

    1. (i)Find the volume of the bigger cylindrical part.[1]
    2. (ii)Find the curved surface area of the bigger cylindrical part.[1]
    3. (iii)(a)Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.[2]
    4. (iii)(b) [OR]Find the sum of the curved surface areas of the two identical smaller cylindrical parts.[2]
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    (i) The volume of the bigger cylindrical part is $462{\text{cm}}^3$; (ii) Its curved surface area is $264{\text{cm}}^2$; (iii)(a) The required ratio is $40:3$; (iii)(b) The sum of the curved surface areas of the two smaller parts is $66{\text{cm}}^2$.

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17. Q157 CBSE 2024
    The ratio of total surface ​area of ​a solid hemisphere ​to ​the ​square ​of its radius is :

    1. (a)$2\pi :1$
    2. (b)$4\pi :1$
    3. (c)$3\pi :1$
    4. (d)$1:4\pi$
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    (c) $3\pi :1$

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18. Q158 CBSE 2024
    A cap ​is cylindrical in ​shape, surmounted by a conical top. If the volume of the ​cylindrical part is equal to that of the conical part, then ​the ratio of the height of the cylindrical part to the ​height of ​the conical part ​is :

    1. (a)$1:2$
    2. (b)$1:3$
    3. (c)$2:1$
    4. (d)$3:1$
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    (b) $1:3$

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19. Q159 CBSE 2024
    If the ​volume of a ​sphere ​is $\frac{11}{21}$ cm${}^3$, then the ​radius of ​the sphere is ​:

    1. (a)$2$ cm
    2. (b)$4$ cm
    3. (c)$\frac{1}{2}$ cm
    4. (d)$\frac{1}{4}$ cm
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    (c) $\frac{1}{2}$ cm

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20. Q160 CBSE 2024
    A hemispherical bowl is ​made of steel of thickness $0.30$ cm. ​The ​inner radius ​of the ​bowl is 3 ​cm. The volume of steel used (in cu cm) ​is:

    1. (a)$595.8\pi$
    2. (b)$5.958\pi$
    3. (c)$6\pi$
    4. (d)$59.58\pi$
    Show answer

    (b) $5.958\pi$

    Step-by-step solution →