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 19 of 20

1. Q361 CBSE 2016
   A ​well of diameter 4 m is dug 21 m deep. ​The earth taken out of ​it has been spread ​evenly all around it in the ​shape of a circular ring of width 3 m ​to form an embankment. Find ​the height of the embankment.
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   The height of the embankment is $4$ m.

   Step-by-step solution →
2. Q362 CBSE 2016
   The sum of ​the radius of base and ​height ​of a solid right ​circular cylinder is 37 cm. If ​the total surface area of the solid cylinder ​is 1628 sq. cm, ​find the volume of the cylinder. $\left(\text{use }\pi =\frac{22}{7}\right)$
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   The volume of the cylinder is $4620{\text{ cm}}^3$ (with $r=7$ cm, $h=30$ cm).

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3. Q363 CBSE 2016
   A metal ​container, open from the top, is in the shape of a frustum of a cone ​of height $21$ cm with radii of its lower and ​upper circular ends as $8$ cm and $20$ cm ​respectively. Find the cost of milk which ​can completely fill the container at the ​rate of $\text{₹}35$ per litre. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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   The cost of milk to fill the container is $\text{₹}480.48$.

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4. Q364 CBSE 2016
   A ​sphere of diameter $12$ cm, is dropped in a ​right ​circular cylindrical vessel, partly filled with water. If ​the ​sphere ​is completely submerged in water, the water level in ​the cylindrical vessel rises by $3\frac{5}{9}$ cm. Find the diameter of the cylindrical vessel.
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   The diameter of the cylindrical vessel is $18$ cm.

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5. Q365 CBSE 2016
   A ​cone of maximum size is ​carved out from a solid cube of side $14$ ​cm. Find the total surface area ​of ​the ​remaining solid ​left ​out.
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   Total surface area $=1022+154\sqrt{5}\approx 1366.4{\text{ cm}}^2$.

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6. Q366 CBSE 2016
   How many silver coins $1.75$ ​cm ​in diameter and of thickness $2$ ​mm, must be melted to ​form a cuboid of ​dimensions $5.5$ ​cm $\times$ $10$ cm $\times$ $3.5$ cm?
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   $400$ silver coins must be melted.

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7. Q367 CBSE 2016
   Due to heavy floods in ​a state, thousands were rendered homeless. $50$ schools collectively offered to the state government to ​provide place and the canvas for $1500$ tents to be fixed ​by the government and decided to share the whole expenditure equally. The ​lower part of each tent is ​cylindrical of base radius $2.8$ m and height $3.5$ m, with conical upper ​part of same base radius but of height $2.1$ m. If the canvas used to make ​the tents costs $\overline{\text{₹}}120$ per sq.m, find the amount shared by each school to set up the tents. What value is generated by the above problem ? (Use $\pi =\frac{22}{7}$)
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   Each school shares $\overline{\text{₹}}332,640$. The value generated is social responsibility / helping the needy.

   Step-by-step solution →
8. Q368 CBSE 2016
   Due ​to heavy floods in a state, thousands were rendered homeless. $50$ ​schools ​collectively offered to the state government to provide place and the canvas for $1500$ tents to be fixed by the ​government and decided to share the whole ​expenditure equally. The lower part of each tent is cylindrical of base radius $2.8$ m and height $3.5$ ​m, with conical upper part of same base radius but of height $2.1$ m. If the canvas used to make the tents costs ₹$120$ per sq. m, find the amount shared by each school to set ​up the tents. What value is generated by the above problem? (Use $\pi =\frac{22}{7}$.)
   Show answer

   Each school shares ₹$332,640$. The value generated is social responsibility, cooperation and concern (helpfulness towards flood victims).

   Step-by-step solution →
9. Q369 CBSE 2016
   Due to heavy floods in a state, thousands were rendered homeless. $50$ schools collectively offered to the state government to provide place and ​the canvas for $1500$ tents ​to be ​fixed by the government and decided to ​share the whole expenditure equally. The lower part of each tent is cylindrical of base radius $2.8$ ​m and height $3.5$ m, with conical upper part of same base radius but of height $2.1$ m. If the canvas used ​to make the tents costs $\text{₹}120$ ​per sq.m, find the amount shared by each school to set up the tents. What ​value is generated by the above problem? (Use $\pi =\frac{22}{7}$)
   Show answer

   Each school shares $\text{₹}3,32,640$. The value generated is concern for fellow citizens and cooperative social responsibility (helping flood victims).

   Step-by-step solution →
10. Q370 CBSE 2016
    Water flows at the rate of $10$ ​m/minute ​through a cylindrical pipe $5$ mm in diameter. ​How long ​would ​it take to fill a ​conical vessel whose diameter at the base is $40$ cm and height $24$ ​cm ?
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    It takes $51.2$ minutes, i.e. $51$ minutes $12$ seconds, to fill the vessel.

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11. Q371 CBSE 2016
    A $20$ m deep well with diameter $7$ m is dug and the ​earth from ​digging is ​evenly spread ​to form a ​platform $22$ m $\times 14$ ​m. Find ​the height of the ​platform.
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    The height of the platform is $2.5$ m.

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12. Q372 CBSE 2016
    In Fig. $9$ is shown a right circular cone ​of height $30$ cm. A small cone ​is cut ​off from the ​top by a plane parallel to the base. If the volume of the small cone is $\frac{1}{27}$ of the ​volume ​of given cone, find at ​what ​height above the base is the section made.

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    The section is made at a height of $20$ cm above the base.

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13. Q373 CBSE 2016
    Find the volume ​of the ​frustum of ​a ​cone $45$ ​cm ​high and whose circular ​ends are of radii $28$ cm ​and $7$ cm.
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    Volume of the frustum $=48510$ cm${}^3$.

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14. Q374 CBSE 2016
    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 and the ​area of metal sheet ​used in making the bucket. ​(use $\pi =3.14$)
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    Height $=15$ cm; area of metal sheet $=2160.32$ cm${}^2$.

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15. Q375 CBSE 2015
    Write the number of solid cubes ​of side $3$ ​cm ​which can be ​cut from a ​solid cube ​of ​side $9$ cm.
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    $27$ cubes

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16. Q376 CBSE 2015
    Due to sudden floods, ​some welfare associations jointly requested the government to get $100$ tents fixed immediately and offered to contribute $50\%$ of the cost. If the lower ​part of each ​tent is of the form of a ​cylinder of ​diameter $4.2$ m and height $4$ m with the conical upper part of same ​diameter but of height $2.8$ m, ​and the canvas to be used costs ₹$100$ per sq. m, find the amount, the associations will have to pay. What values are shown by these ​associations? [Use $\pi =\frac{22}{7}$]
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    Canvas per tent $=75.9$ m${}^2$; total cost $=$ ₹$7,59,000$; the associations pay $50\%$ $=$ ₹$3,79,500$. They show values of generosity, social responsibility and concern for flood victims.

    Step-by-step solution →
17. Q377 CBSE 2015
    Two spheres of same metal weigh $1$ kg ​and $7$ kg. The radius of the smaller sphere is $3$ cm. ​The two spheres are melted to form a ​single ​big ​sphere. Find the diameter of the ​new sphere.
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    Diameter of the new sphere $=12$ cm

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18. Q378 CBSE 2015
    A hemispherical ​depression is cut ​out ​from one face of ​a solid cubical block of ​side $28$ cm, such that the diameter of the ​hemisphere ​is equal to the ​edge of the cube. Determine the surface area of the remaining solid. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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    The surface area of the remaining solid is $5320{\text{ cm}}^2$.

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19. Q379 CBSE 2015
    In Fig. ​4, from the top of ​a ​solid cone of height $12$ ​cm ​and base radius $6$ ​cm, a cone of height $4$ cm is removed by a plane parallel to the base. Find the total surface ​area of the ​remaining solid. $\left(\text{Use }\pi =\frac{22}{7}\text{ and }\sqrt{5}=2.236\right)$

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    The total surface area of the remaining solid is about $350.59$ cm².

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20. Q380 CBSE 2015
    A hemispherical ​bowl of ​internal diameter $36$ cm contains ​liquid. This liquid is ​filled into $72$ ​cylindrical bottles of diameter $6$ ​cm. Find the ​height of the each ​bottle, if $10\%$ liquid is wasted in this transfer.
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    Height of each bottle $=5.4$ cm.

    Step-by-step solution →