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 6 of 20

1. Q101 CBSE 2026
   A pen stand ​is made up of wood and is in the shape of a cuboid with four conical depressions and cylindrical extensions to hold pens. The depressions are hollowed out from the wooden cuboidal stand and cylindrical extensions are made up of metal attached separately ​as shown in ​the figure given below : The dimensions of the cuboidal block of wood ​are $15$ ​cm $\times$ $10$ cm $\times$ $3.5$ cm. The radius of each conical depression is $0.5$ cm and depth is $1.4$ cm. The radius ​and height of each cylindrical metal extension are $0.5$ cm and $4.9$ cm ​respectively.

   1. (i)Find the volume of wood in the entire stand.
   2. (ii)Find the inner surface ​area of a conical depression along with that of the cylindrical extension. (Use $\sqrt{221}=14.8$)

   Show answer

   (i) The volume of wood in the stand is $\frac{7853}{15}\approx 523.53{\text{cm}}^3$; (a)(ii) The inner surface area of one conical depression together with its cylindrical extension is $2.33+15.4=17.73{\text{cm}}^2$

   Step-by-step solution →
2. Q102 CBSE 2026
   A solid is in ​the ​shape of a cylinder with a solid ​hemisphere attached to one of its ends as ​shown in the figure. Let the height and diameter of the cylinder be same (say $H$). Prove that the volume of the solid shown ​in the figure is same as the volume of ​a cone of height $H$ and diameter $2H$. Also find the ​total surface area of the solid in ​terms of $H$.

   Show answer

   The volume of the solid is $\frac{\pi H^3}{3}$, which is exactly the volume of a cone of height $H$ and diameter $2H$, and its total surface area is $\frac{7\pi H^2}{4}$.

   Step-by-step solution →
3. Q103 CBSE 2026
   From a ​solid cylinder whose ​height is $2.8$ cm and radius $2.1$ cm, a conical cavity of the same height and same ​radius is hollowed out. ​Find ​the ​volume and the total surface ​area of the remaining solid.
   Show answer

   Volume of the remaining solid $=25.872{\text{cm}}^3$ and its total surface area $=73.92{\text{cm}}^2$.

   Step-by-step solution →
4. Q104 CBSE 2026
   There are many varieties of mushrooms available in the world. One such ​mushroom ​'Amanita muscaria' has ​an upper part which is like a red cap (hemispherical) and a lower part which is like a white stem (cylindrical). The hemispherical cap's ​radius $=3$ cm and the cylindrical ​stem is $2$ cm high ​with diameter $1.4$ cm. Considering the mushroom a ​solid object, answer ​the following questions:

   1. (i)What is the total height of a mushroom?
   2. (ii)Find the volume of the stem.
   3. (iii)(a) Determine the volume of 7 such mushrooms. OR (b) Find the total surface area of 7 such mushrooms.
   Show answer

   (i) Total height $=5$ cm. (ii) Volume of the stem $=3.08$ cm³. (iii)(a) Volume of 7 mushrooms $=417.56$ cm³, OR (b) Total surface area of 7 mushrooms $=655.6$ cm².

   Step-by-step solution →
5. Q105 CBSE 2026
   A wall mounted lamp, made of fabric, is ​shown below. Lamp ​has cuboidal shape, open from top and bottom. A spherical ​bulb of diameter $7$ cm is ​latched ​with a ​very thin rod. (Ignore the rod ​while making calculations.) Dimensions of the cuboid are $24$ cm $\times$ $12$ ​cm $\times$ $17$ cm.

   1. (i)Find the surface area of the bulb.[1]
   2. (ii)What could be the maximum diameter of the bulb if at least $1$ cm space is left from each side?[1]
   3. (iii) (a)Find the area of the fabric used if there is a fold of $2$ cm on top and bottom edges.[2]
   4. (iii) (b)Find the space available inside the lamp.[2]
   Show answer

   (i) Surface area of the bulb $=154$ cm${}^2$; (ii) maximum diameter of the bulb $=10$ cm; (iii)(a) area of the fabric used $=1512$ cm${}^2$; (iii)(b) space available inside the lamp $=\frac{14149}{3}\approx 4716.33$ cm${}^3$.

   Step-by-step solution →
6. Q106 CBSE 2026
   As a part of school project, Mishika and Sahaj created a ​bird-bath from the cylindrical log of wood by scooping out the hemispherical depression from one end of the cylinder as shown in the figure given below. Cylinder has a length $2$ m out of ​which $0.6$ ​m is in earth and ​the diameter is $1.4$ ​m. On the basis ​of the above information, answer the following questions ​:

   1. (i)Write the radius of the hemispherical depression.[1]
   2. (ii)Find the volume of water that can be filled in the hemispherical depression in terms of $\pi$.[1]
   3. (iii)(a)Find the total surface area of log of wood above the ground after making the bird-bath.[2]
   4. (iii)(b)OR : Compute the volume of log of wood above the ground after making the bird-bath.[2]
   Show answer

   (i) The radius of the hemispherical depression is $0.7$ m; (ii) The depression can hold $\frac{2}{3}\pi (0.7{)}^3=\frac{343\pi }{1500}\approx 0.229\pi {\text{ m}}^3$ of water; (iii)(a) The total surface area of the log above the ground is $9.24{\text{ m}}^2$; (iii)(b) The volume of the log of wood above the ground is approximately $1.437{\text{ m}}^3$.

   Step-by-step solution →
7. Q107 CBSE 2026
   On a ​Sunday your ​parents took you to a ​fair. You could see lot of ​toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream ​for you. Based on the information given above, ​answer ​the following questions :

   1. (i)Find the length of the diagonal of Rubik's cube if each edge measures $6$ cm.[1]
   2. (ii)Find the volume of Rubik's cube if the length of the edge is $7$ cm.[1]
   3. (iii)(a)What is the curved surface area of hemisphere (ice-cream) if the base radius is $7$ cm ?[2]
   4. (iii)(b)OR — If two cubes of edges $4$ cm are joined end-to-end, then find the surface area of the resulting cuboid.[2]
   Show answer

   (i) The length of the diagonal of the Rubik's cube is $6\sqrt{3}\approx 10.39$ cm; (ii) The volume of the Rubik's cube is $343{\text{cm}}^3$; (iii)(a) The curved surface area of the hemisphere is $308{\text{cm}}^2$; (iii)(b) OR — The surface area of the resulting cuboid is $160{\text{cm}}^2$.

   Step-by-step solution →
8. Q108 CBSE 2026
   In a ​coffee shop, coffee is served in two types of cups. One ​is cylindrical in shape with each of diameter $8$ ​cm and height $7$ cm, and the other ​hemispherical ​with each of diameter $14$ ​cm. Based on the ​above, answer the following ​questions:

   1. (i)What is the outer curved surface area of the cylindrical cup?
   2. (ii)What is the inner surface area of the hemispherical cup?
   3. (iii)(a)Find the difference of the capacities of the two cups.
   4. (iii)(b)OR: Find the total volume of coffee in two cylindrical and one hemispherical cup.
   Show answer

   (i) Outer curved surface area of the cylindrical cup $=176{\text{cm}}^2$; (ii) Inner surface area of the hemispherical cup $=308{\text{cm}}^2$; (iii)(a) Difference of capacities $=\frac{1100}{3}\approx 366.67{\text{cm}}^3$ (the hemispherical cup holds more); (iii)(b) Total volume of coffee $=\frac{4268}{3}\approx 1422.67{\text{cm}}^3$.

   Step-by-step solution →
9. Q109 CBSE 2026
   A model of Leafy Ball Fountain is made to be kept on the ​tabletop. Water gently cascades down ​the ​ball into a decorative cylindrical pool where it is recycled. The diameter of the spherical ball is $21$ cm. For the cylindrical pool, the outer ​diameter ​is $50$ cm and the inner ​diameter is $40$ cm. The height of the solid base is $14$ cm and the height of the water filled ​is $7$ cm. Observe the figure and answer ​the following questions:

   1. (i)Determine the total height of the fountain.[1]
   2. (ii)Find the volume of the ball.[1]
   3. (iii)(a)If one-third of the ball is submerged in the water, find the volume of the water filled in the pool.[2]
   4. (iii)(b)(OR) Find the sum of the outer curved surface area of the cylindrical part and surface area of the ball.[2]
   Show answer

   (i) The total height of the fountain is $35$ cm. (ii) The volume of the ball is $4851{\text{cm}}^3$. (iii)(a) The volume of water filled is $7183{\text{cm}}^3$. (iii)(b) The sum of the outer curved surface area and the ball's surface area is $4686{\text{cm}}^2$.

   Step-by-step solution →
10. Q110 CBSE 2026
    'Gilli Danda' is ​a very popular traditional ​game of ​India which is played ​with ​two wooden sticks ​— the larger one is called ​'Danda' and the smaller one 'Gilli'. 'Danda' — It is cylindrical in shape with diameter $4$ cm and length $42$ cm. Gilli — It is cylindrical in the middle with identical conical ends of the same radius $1.5$ cm and length $2.8$ cm. The length of the cylindrical part is $7$ cm. Based on the above, answer ​the following questions:

    1. iFind the volume of wood used in making both the conical parts of Gilli.[1]
    2. iiFind the volume of wood used in making the cylindrical part of Gilli.[1]
    3. iii(a) A cylindrical log of wood of radius $1.5$ cm and length $14$ cm is used to make Gilli. Find the volume of the wood scrapped. OR (b) Find the total surface area of 'Danda'.[2]
    Show answer

    (i) Volume of both conical parts $=13.2{\text{cm}}^3$; (ii) Volume of the cylindrical part $=49.5{\text{cm}}^3$; (iii)(a) Volume of wood scrapped $=36.3{\text{cm}}^3$, OR (b) Total surface area of Danda $=\frac{3872}{7}\approx 553.14{\text{cm}}^2$.

    Step-by-step solution →
11. Q111 CBSE 2026
    For a cricket tournament involving $8$ countries, a special ​trophy, as shown below, is ​designed. The ​height and diameter of the cylindrical part are $14$ cm and $6$ cm respectively and the ​diameter of the spherical ball on the top ​is $7$ ​cm. Based on ​the above information, ​answer the following questions :

    1. (i)Find the total height of the trophy excluding the wooden part.[1]
    2. (ii)Find the difference between the radius of sphere and that of cylinder.[1]
    3. (iii)(a)If the cylindrical part and spherical part are separated and gold plated overall, find the total surface area to be gold plated.[2]
    4. (iii)(b)OR : Find the volume of the metal used in making the trophy, assuming that the metal is completely filled in it.[2]
    Show answer

    (i) The total height of the trophy excluding the wooden part is $21$ cm; (ii) The difference between the radius of the sphere and that of the cylinder is $0.5$ cm; (iii)(a) The total surface area to be gold plated is $\frac{3322}{7}\approx 474.57{\text{cm}}^2$; (iii)(b) The volume of the metal used is $\frac{1727}{3}\approx 575.67{\text{cm}}^3$.

    Step-by-step solution →
12. Q112 CBSE 2025
    Two ​identical cones are joined as shown ​in the figure. ​If ​the radius of the base ​is $4$ cm ​and the slant height of each cone is $6$ cm, ​then ​the height of the solid is

    1. (a)$8$ cm
    2. (b)$4\sqrt{5}$ cm
    3. (c)$2\sqrt{5}$ cm
    4. (d)$12$ cm
    Show answer

    (b) $4\sqrt{5}$ cm

    Step-by-step solution →
13. Q113 CBSE 2025
    Two right ​circular cylinders of equal volumes have ​their ​heights in the ​ratio $1:2$. The ​ratio ​of their ​radii is :

    1. (a)$\sqrt{2}:1$
    2. (b)$1:2$
    3. (c)$1:4$
    4. (d)$1:\sqrt{2}$
    Show answer

    (a) $\sqrt{2}:1$

    Step-by-step solution →
14. Q114 CBSE 2025
    The largest possible cone is just fitted inside ​a ​hollow cube of edge $25$ cm. ​The ​radius of the base of the ​cone is

    1. (a)$5$ cm
    2. (b)$12.5$ cm
    3. (c)$25$ cm
    4. (d)$10$ cm
    Show answer

    (b) $12.5$ cm

    Step-by-step solution →
15. Q115 CBSE 2025
    On ​the top face of ​the wooden cube of ​side $7$ cm, ​hemispherical depressions of radius $0.35$ cm ​are to be formed by taking out ​the wood. The maximum number of depressions that can be formed is:

    1. (a)$400$
    2. (b)$100$
    3. (c)$20$
    4. (d)$10$
    Show answer

    (b) $100$

    Step-by-step solution →
16. Q116 CBSE 2025
    If the ​volumes of two cubes are in the ratio $8:125$, then the ​ratio ​of ​their ​surface areas ​is ​:

    1. (a)$8:125$
    2. (b)$4:25$
    3. (c)$2:5$
    4. (d)$16:25$
    Show answer

    (b) $4:25$

    Step-by-step solution →
17. Q117 CBSE 2025
    If a ​cone of greatest possible ​volume is hollowed out from a solid ​wooden cylinder, then the ratio ​of ​the ​volume of ​remaining wood to the volume ​of cone hollowed out is

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

    (c) $2:1$

    Step-by-step solution →
18. Q118 CBSE 2025
    For ​which of the following solids is the ​lateral/curved surface ​area and ​total surface area the same?

    1. (a)Cube
    2. (b)Cuboid
    3. (c)Hemisphere
    4. (d)Sphere
    Show answer

    (d) Sphere

    Step-by-step solution →
19. Q119 CBSE 2025
    A ​cylindrical pencil ​sharpened ​at ​one edge ​is a ​combination of:

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

    (c) a cylinder and a cone

    Step-by-step solution →
20. Q120 CBSE 2025
    A cone of height 12 cm and slant height 13 cm ​is ​surmounted ​on a hemisphere having ​radius equal to that of ​cone. The ​entire height of ​the solid is

    1. (a)$17$ cm
    2. (b)$18$ cm
    3. (c)$22$ cm
    4. (d)$23$ cm
    Show answer

    (a) $17$ cm

    Step-by-step solution →