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 20 of 20

1. Q381 CBSE 2015
   A solid wooden toy is in the form of ​a hemisphere surmounted by a cone of same radius. ​The radius of hemisphere is $3.5$ cm and ​the total wood used in ​the making of ​toy is $166\frac{5}{6}$ cm${}^3$. Find the ​height of the toy. Also, find the cost of painting the hemispherical part of ​the ​toy at the rate of $\text{₹}10$ per cm${}^2$. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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   Height of the toy $=9.5$ cm; cost of painting the hemispherical part $=\text{₹}770$.

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2. Q382 CBSE 2015
   A $14$ m deep well with diameter $8$ m is dug ​and the earth from digging is evenly spread out ​to form a platform $11$ ​m $\times$ $8$ m. Find ​the height ​of ​the platform. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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   The height of the platform is $8$ m.

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3. Q383 CBSE 2015
   A metallic cylinder ​has radius 3 cm and height 5 cm. To reduce ​its weight, ​a ​conical hole ​is drilled in the cylinder. The conical hole has ​a radius of $\frac{3}{2}$ cm and its depth is $\frac{8}{9}$ cm. Calculate the ratio of ​the ​volume of metal left in the cylinder to the volume of metal taken out in conical shape.
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   The ratio of metal left to metal taken out is $133:2$.

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4. Q384 CBSE 2015
   A cubical block of side $10$ cm is surmounted by a ​hemisphere. What is the largest ​diameter that the hemisphere can have? Find the cost of painting ​the ​total surface area ​of the solid so formed, at the rate of ​₹$5$ per $100$ sq. cm. ​[Use $\pi =3.14$]
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   Largest diameter $=10$ cm; painted area $=678.5$ cm${}^2$; cost $\approx$ ₹$33.93$ (exactly ₹$33.925$).

   Step-by-step solution →
5. Q385 CBSE 2015
   In Fig. 5, from a ​cuboidal solid metallic block, of dimensions $15$ cm $\times 10$ cm $\times 5$ ​cm, ​a cylindrical hole of diameter $7$ cm ​is drilled ​out. ​Find the surface area of ​the remaining block. $\left[\text{Use }\pi =\frac{22}{7}\right]$

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   Surface area of the remaining block $=583$ cm${}^2$.

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6. Q386 CBSE 2015
   A solid right-circular cone ​of height ​60 cm and radius ​30 cm is dropped ​in a right-circular cylinder full of water of height 180 ​cm ​and radius 60 cm. Find the ​volume of water left in the cylinder, in cubic metres. ​[Use $\pi =\frac{22}{7}$]
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   The volume of water left in the cylinder is $1.98{\text{ m}}^3$.

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7. Q387 CBSE 2015
   $504$ cones, each ​of ​diameter $3.5$ cm and height $3$ ​cm, are melted and recast into a metallic sphere. Find the ​diameter of ​the sphere and hence find ​its surface ​area. [Use $\pi =\frac{22}{7}$]
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   Diameter $=21$ cm; surface area $=1386$ cm${}^2$.

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8. Q388 CBSE 2015
   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 ​required?
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   Irrigated area $=300000$ m${}^2=30$ hectares.

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9. Q389 CBSE 2015
   A well of ​diameter $4$ m is dug $14$ ​m deep. The earth taken ​out is spread evenly all around the well ​to ​form a $40$ cm high embankment. Find ​the width of ​the embankment.
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   The width of the embankment is $10$ m.

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10. Q390 CBSE 2015
    A vessel full of water is ​in the form ​of an inverted ​cone of height 8 cm and the radius of its top, which is open, ​is 5 cm. 100 ​spherical lead balls ​are ​dropped into the vessel. One-fourth of the water flows out of the vessel. Find the radius of a ​spherical ball.
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    The radius of each spherical lead ball is $\frac{1}{2}$ cm, i.e. $0.5$ cm.

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11. Q391 CBSE 2015
    Water ​is flowing at the rate of $2.52$ km/h through a cylindrical pipe ​into a cylindrical ​tank, the radius of whose base ​is $40$ cm. If ​the increase in the ​level of water in the tank, in half an hour is $3.15$ m, find ​the internal ​diameter of the pipe.
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    The internal diameter of the pipe is $4$ cm.

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12. Q392 CBSE 2015
    From each end of a solid metal cylinder, metal was ​scooped out in ​hemispherical form of same diameter. The height of the cylinder is $10$ cm and its base ​is of radius $4.2$ cm. ​The rest ​of ​the ​cylinder is melted and converted into a cylindrical wire of $1.4$ cm thickness. Find the length of ​the wire. [Use $\pi =\frac{22}{7}$]
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    Length of the wire $=158.4$ cm.

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13. Q393 CBSE 2015
    Milk in a container, which is in the form of a frustum of a cone of height 30 cm and the radii of whose lower and upper circular ends are ​20 cm and 40 cm respectively, is to ​be distributed in a camp for flood victims. If ​this milk is ​available at the rate of $\text{₹}35$ per litre ​and 880 litres of milk is needed daily for a camp, find how ​many such containers of milk are needed for a camp and what cost will ​it put on the ​donor agency for this. What value is indicated through this by the donor agency?
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    10 containers are needed; the cost to the donor agency is $\text{₹}30800$. The value indicated is kindness, generosity, and concern for humanity (helping flood victims).

    Step-by-step solution →