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 13 of 20

1. Q241 CBSE 2022
   A cubical block of side $7$ cm is surmounted by ​a ​hemisphere ​of largest possible diameter as shown in Figure 1. Find the total ​surface area of ​the solid.

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   Total surface area $=332.5$ cm${}^2$

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2. Q242 CBSE 2022
   150 spherical ​marbles, each of ​diameter $1.4$ ​cm, are dropped in a cylindrical vessel of diameter ​7 cm containing some water, and are completely immersed in water. Find the rise in ​the ​level ​of water in the ​cylindrical vessel.
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   The water level rises by $5.6$ cm.

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3. Q243 CBSE 2022
   How many solid cones ​of height $3$ cm ​and radius $2$ cm ​can be formed by melting ​a solid ​sphere of ​radius $3$ ​cm?
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   $9$ cones

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4. Q244 CBSE 2022
   Three ​cubes ​of side 6 ​cm each, ​are ​joined as shown in Figure 1. Find the total surface ​area of the ​resulting cuboid.

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   Total surface area $=504{\text{ cm}}^2$.

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5. Q245 CBSE 2022
   The ​curved surface area ​of a ​right ​circular cylinder ​is 176 ​sq ​cm ​and its volume is 1232 cu cm. What is the height of the cylinder ?
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   The height of the cylinder is $h=2$ cm.

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6. Q246 CBSE 2022
   Find the curved surface ​area ​of ​a right circular ​cone whose ​height ​is $15$ cm and ​base radius is $8$ cm. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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   CSA $=\frac{2992}{7}\approx 427.43$ cm${}^2$

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7. Q247 CBSE 2022
   The surface ​area of ​a sphere ​is $616$ ​sq cm. Find ​its radius. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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   $r=7$ cm

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8. Q248 CBSE 2022
   The largest ​sphere ​is ​carved out of ​a solid cube of side 21 cm. ​Find the ​volume of the ​sphere.
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   The volume of the sphere is $4851{\text{ cm}}^3$.

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9. Q249 CBSE 2022
   A solid ​copper rod of diameter $1$ cm and ​length $8$ ​cm is ​drawn into ​a wire of length $18$ ​cm of ​uniform thickness. Find the thickness of the wire.
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   Thickness $=\frac{2}{3}$ cm $\approx 0.67$ cm

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10. Q250 CBSE 2022
    The ​radius of the base ​and the height of a solid right ​circular cylinder are ​in the ​ratio $2:3$ and its ​volume ​is $1617$ cm${}^3$. Find the total ​surface area of the cylinder. (Take $\pi =\frac{22}{7}$)
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    Total surface area $=770$ cm${}^2$

    Step-by-step solution →
11. Q251 CBSE 2022
    A ​solid metallic sphere ​of radius $10.5$ cm is melted ​and ​recast into a number ​of smaller solid cones, ​each of radius $3.5$ cm and ​height $3$ cm. Find the number of cones so ​formed.
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    Number of cones $=126$

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12. Q252 CBSE 2022
    Three metallic ​spheres of radii $6$ ​cm, $8$ cm and $10$ cm ​respectively, ​are melted to form a single solid ​sphere. ​Find ​the radius of the resulting sphere.
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    $R=12$ cm

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13. Q253 CBSE 2022
    A canal is $300$ cm wide and $120$ cm ​deep. The water in ​the ​canal is flowing ​with a speed of $20$ km/h. How much area will it ​irrigate in $20$ minutes, if $8$ cm of ​standing water is desired?
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    Area irrigated $=300000$ m${}^2$ (i.e. $30$ hectares)

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14. Q254 CBSE 2022
    A solid ​toy is in the ​form of ​a ​hemisphere surmounted by a right ​circular cone of same radius. The height of the cone ​is $2$ cm and the diameter ​of the base is $4$ cm. Find the volume of the toy.
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    $V=8\pi \approx 25.14$ cm${}^3$

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15. Q255 CBSE 2022
    A spherical ​glass vessel has a ​cylindrical ​neck 8 cm long and 1 cm in radius. The radius of the spherical ​part is 9 cm. Find the amount of water ​(in litres) ​it ​can hold, when filled completely. $\left(\text{Take }\pi =\frac{22}{7}\right)$
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    The vessel holds $3.08$ litres of water.

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16. Q256 CBSE 2022
    From a solid cylinder of height $30$ cm and radius $7$ ​cm, ​a conical cavity of height $24$ ​cm and same radius is hollowed out. ​Find ​the total surface ​area of the ​remaining solid.
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    Total surface area $=2024$ cm${}^2$

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17. Q257 CBSE 2022
    Water ​in ​a canal, $8$ m wide and $6$ ​m deep, is flowing with a speed of $12$ km/hour. How ​much area will ​it irrigate in one hour, if $0.05$ m ​of standing water is required ​?
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    Area irrigated $=11520000$ m${}^2$ ($=1152$ hectares)

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18. Q258 CBSE 2022
    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. $\left(\text{Take }\pi =\frac{22}{7}\right)$
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    Total surface area of the remaining solid $=17.6{\text{ cm}}^2$.

    Step-by-step solution →
19. Q259 CBSE 2022
    The technique of ​Rainwater harvesting through Recharge pit is ​very useful. Rainwater is collected on the roof and ​then flowing through the ​Recharge pit it goes to the ground. Observe the picture given ​above. ​The surface area of the roof floor is $100$ m${}^2$. The cuboidal pit measures $3$ m $\times 3$ m $\times 2$ ​m. (Breadth $=3$ m, Depth $=2$ ​m, Length $=3$ m.)

    1. aWater standing on the roof is released into the cuboidal pit. If the cuboidal pit is filled completely by the roof water, then find the height of standing water on the roof.[2]
    2. bInstead of a cuboidal pit, if a cylindrical pit with diameter $3$ m and height $2$ m had been built, then which tank would hold more water?[2]
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    (a) Height of standing water $=0.18$ m ($18$ cm). (b) The cuboidal pit ($18$ m${}^3$) holds more water than the cylindrical pit ($\approx 14.14$ m${}^3$).

    Step-by-step solution →
20. Q260 CBSE 2022
    Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea-sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as 'The Ceramic ​Town'. One of the private schools of ​Bulandshahr organised an ​Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following ​are the few pottery objects of ​Khurja. Students found the shapes of the objects very interesting and they could ​easily relate them with mathematical ​shapes viz sphere, hemisphere, cylinder etc. Maths teacher who was ​accompanying the students asked following questions.

    1. aThe internal radius of hemispherical bowl (I) is 9 cm and the radius and height of cylindrical jar (II) are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied into cylindrical jars, then how many cylindrical jars are required?[2]
    2. bIf in the cylindrical jar full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar?[2]
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    (a) 54 cylindrical jars are required. (b) Water that flows out $=3\pi =\frac{66}{7}\approx 9.43$ cm${}^3$.

    Step-by-step solution →