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 15 of 20

1. Q281 CBSE 2020
   $500$ persons ​are ​taking dip into a cuboidal pond which is $80$ m long ​and $50$ m broad. What is ​the ​rise of ​water level in the pond, ​if the average displacement ​of the water by a person is $0.04$ m${}^3$?
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   The water level rises by $0.005$ m, i.e. $0.5$ cm.

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2. Q282 CBSE 2020
   A solid sphere of ​radius $10.5$ ​cm is melted and recast into smaller ​cones ​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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3. Q283 CBSE 2020
   The surface area ​of a solid metallic sphere ​is $616{\text{ cm}}^2$. It is ​melted and recast ​into ​a cone of height $28$ cm. ​Find the diameter of ​the base of the cone ​so formed.
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   The diameter of the cone's base is $14$ cm.

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4. Q284 CBSE 2020
   A bucket, open at the top, is in the form of a ​frustum of ​a cone with ​a capacity ​of $12308.8$ ​cm${}^3$. The radii ​of the top and bottom circular ends are $20$ cm and $12$ cm respectively. Find the height of the bucket. (Use $\pi =3.14$)

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   The height of the bucket is $h=15$ cm.

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5. Q285 CBSE 2020
   A ​conical vessel ​whose internal radius is $5$ cm and ​height $24$ cm is full of water. ​This water is emptied into a cylindrical ​vessel of internal radius $10$ ​cm. Find the ​height to which water level rises ​in the cylindrical vessel.
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   The water rises to a height of $2$ cm in the cylindrical vessel.

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6. Q286 CBSE 2020
   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 $10$ cm and the radius of the ​base is $7$ cm. Determine ​the volume of the toy. ​Also find ​the area ​of the ​coloured sheet required to cover the toy. (Use $\pi =\frac{22}{7}$ and $\sqrt{149}=12.2$)
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   Volume of the toy $=1232$ cm³ and the area of the coloured sheet required $=576.4$ cm².

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7. Q287 CBSE 2020
   A bucket ​is ​in the form ​of a frustum of a cone of height 30 cm ​with ​the radii of ​its lower and upper circular ends as 10 cm and 20 cm respectively. Find the capacity of the ​bucket. (Use $\pi =3.14$)
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   Capacity of the bucket $=21980$ cm³ (i.e. $21.98$ litres).

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8. Q288 CBSE 2020
   Water in ​a canal ​6 m wide and ​1.5 m ​deep, is flowing with ​a ​speed of 10 km/hr. How ​much area will it irrigate in 30 minutes if 4 cm of standing water is needed?
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   Area irrigated $=1125000$ m² $=112.5$ hectares.

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9. Q289 CBSE 2020
   A bucket is in the form ​of a frustum of a cone of height $30$ cm ​with radii of ​its lower and upper ends as $10$ cm and $20$ cm, respectively. Find ​the capacity of the bucket. ​Also find the cost ​of milk which can ​completely fill the bucket ​at the rate of Rs. $40$ per litre. $\left(\text{Use }\pi =\frac{22}{7}\right)$
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   Capacity of the bucket $=22$ litres; cost of milk to fill it $=22\times 40=$ Rs $880$.

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10. Q290 CBSE 2020
    A bucket open at the top has top and bottom radii of circular ends as $40$ cm and $20$ ​cm respectively. Find ​the volume of ​the bucket ​if its depth ​is $21$ cm. Also find the area of ​the ​tin sheet required for making ​the bucket. (Use $\pi =\frac{22}{7}$)
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    Volume $=61600$ cm${}^3$ ($=61.6$ litres); tin sheet required $\approx 6725.71$ cm${}^2$.

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11. Q291 CBSE 2020
    A solid iron cuboidal ​block of ​dimensions $4.4\text{ m}\times 2.6\text{ m}\times 1\text{ m}$ ​is cast ​into a hollow cylindrical ​pipe of internal radius $30$ cm ​and thickness $5$ cm. Find the length ​of ​the pipe.
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    The length of the pipe is $112$ m.

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12. Q292 CBSE 2020
    A hemispherical depression is ​cut ​out ​from ​one face of ​a cubical wooden block of edge $21$ ​cm, such that the diameter of the hemisphere is equal ​to edge ​of the cube. Determine the volume of the remaining block.
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    Volume of the remaining block $=9261-2425.5=6835.5$ cm³.

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13. Q293 CBSE 2020
    From a solid cylinder whose height is $15$ cm and ​the ​diameter is $16$ cm, a ​conical cavity of the same height and same ​diameter ​is hollowed out. Find the total surface area of remaining solid. ​(Give your answer in terms of $\pi$)
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    The total surface area of the remaining solid is $440\pi$ cm${}^2$.

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14. Q294 CBSE 2020
    An ​open metal bucket is ​in the shape of a ​frustum of a cone of height $21$ cm with radii of ​its ​lower ​and upper ends as $10$ cm and $20$ cm respectively. ​Find the cost of milk which can ​completely fill the bucket at the rate of ₹40 per litre.
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    Cost of milk $=₹616$ (capacity $15.4$ litres).

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15. Q295 CBSE 2020
    Find the curved surface area of ​the ​frustum of a cone, the diameters of whose circular ​ends ​are $20$ m and $6$ ​m and ​its ​height is $24$ m.
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    Curved surface area $=325\pi =\frac{7150}{7}\approx 1021.43$ m².

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16. Q296 CBSE 2020
    A solid metallic cylinder of diameter $12$ cm and height $15$ ​cm is melted and ​recast ​into $12$ toys in ​the ​shape of a ​right circular cone mounted on a hemisphere of same radius. Find the radius of the hemisphere and total height ​of ​the toy, if the height of the cone is $3$ times the radius.
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    The radius of the hemisphere is $3$ cm and the total height of the toy is $12$ cm.

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17. Q297 CBSE 2020
    A solid is in ​the shape ​of ​a cone surmounted on a hemisphere. The radius of each of them being $3.5$ ​cm and the total height of the ​solid is $9.5$ cm. Find the volume ​of the ​solid.
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    $V\approx 166.83$ cm${}^3$ (i.e. $\frac{500.5}{3}$ cm${}^3$)

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18. Q298 CBSE 2020
    The ​height of ​a cone is $10$ cm. The cone is divided into ​two parts using ​a ​plane parallel to its base at the middle of ​its height. Find the ratio of the ​volumes of the two parts.
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    The ratio of the volumes of the two parts (top cone : bottom frustum) is $1:7$.

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19. Q299 CBSE 2019
    A ​solid is in the form of ​a cylinder with ​hemispherical ends. The total ​height of the solid is $20$ cm and the diameter of the cylinder is $7$ cm. Find the ​total volume of the solid. (Use $\pi =\frac{22}{7}$)
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    Total volume $\approx 680.17$ cm${}^3$ (exactly $\frac{2597}{12}\times \frac{22}{7}=680\frac{1}{6}$ cm${}^3$)

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20. Q300 CBSE 2019
    A cone of height $24$ cm and radius of base $6$ cm is made up ​of ​modelling clay. ​A child reshapes it in the ​form of a sphere. ​Find the radius of ​the sphere and hence ​find ​the surface area of this sphere. $\left(\text{Use }\pi =\frac{22}{7}\right)$
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    Radius of the sphere $=6$ cm; surface area $=144\pi =\frac{3168}{7}\approx 452.57$ cm${}^2$.

    Step-by-step solution →