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 18 of 20

1. Q341 CBSE 2017
   In a rain-water harvesting system, the ​rain-water ​from a roof ​of $22\text{ m}\times 20\text{ m}$ drains into a cylindrical tank having diameter of base $2$ m ​and height $3.5$ m. If the tank is full, find ​the rainfall in cm. Write your views on ​water ​conservation.
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   The rainfall is $2.5$ cm. Rain-water harvesting conserves a precious resource by storing run-off, recharging groundwater and reducing wastage.

   Step-by-step solution →
2. Q342 CBSE 2017
   In ​a rain-water harvesting system, the rain-water ​from a roof ​of $22$ m $\times$ $20$ ​m ​drains into a cylindrical tank having diameter of base $2$ m and height $3.5$ m. If the ​tank is full, ​find the rainfall in cm. Write your views ​on water conservation.
   Show answer

   The rainfall is $2.5$ cm. Water conservation note: harvesting this runoff (11 m${}^3$) recharges groundwater and reduces freshwater demand, so rainwater harvesting should be widely adopted.

   Step-by-step solution →
3. Q343 CBSE 2017
   A well ​of diameter $3$ m ​is ​dug $14$ ​m ​deep. The ​soil taken out of it is spread evenly all ​around it to a width of $5$ m to form an embankment. Find the height ​of the embankment.
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   Height of the embankment $H=0.7875$ m (i.e. about $78.75$ cm).

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4. Q344 CBSE 2017
   A ​container made of ​a metal sheet open at ​the top is of the form ​of a frustum of a cone, ​whose height is $16$ cm ​and the radii of its lower and upper circular edges are $8$ cm and $20$ cm respectively. Find the cost ​of milk at the rate of $\text{₹}35$ per litre which ​can fill it completely.
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   The container holds about $10.46$ litres, costing approximately $\text{₹}366.08$.

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5. Q345 CBSE 2017
   A ​solid metallic sphere, $3$ ​cm ​in radius, is ​melted and ​recast ​into three spherical balls ​with radii $1\times 5$ ​cm, $2$ cm and $x$ cm. Find the value of $x$.
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   $x=2.5$ cm

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6. Q346 CBSE 2017
   A metallic right circular cone $20$ cm high and whose vertical angle is $60^{\circ }$ is cut into two ​parts ​at the middle ​of its height by ​a plane parallel to its base. If the frustum so obtained be drawn ​into a ​wire ​of uniform diameter $\frac{1}{16}$ ​cm, find the length of the wire.
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   Length of the wire $L=\frac{7168000}{9}\approx 796444.4$ cm $\approx 7964.4$ m.

   Step-by-step solution →
7. Q347 CBSE 2017
   The height of a cone is $30$ ​cm. A small cone is cut off at the ​top, at some height above the base, by a plane ​parallel to the ​base. If its volume is $\frac{1}{27}$ of ​the volume ​of the ​given cone, at what height above the base has the section been made?
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   The section is made at a height of $20$ cm above the base.

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8. Q348 CBSE 2017
   In a hospital used water is collected ​in a cylindrical ​tank of diameter $2$ m and height $5$ m. ​After recycling, this water is used to irrigate a park of hospital ​whose length is $25$ m and breadth is $20$ m. If tank is filled completely then ​what will be the height of standing water ​used for ​irrigating the park. ​Write your views on recycling of water.
   Show answer

   Height of standing water $h=\frac{\pi }{100}$ m $=\frac{11}{350}$ m $\approx 0.0314$ m $\approx 3.14$ cm. Recycling water conserves a precious resource and reduces fresh-water demand.

   Step-by-step solution →
9. Q349 CBSE 2016
   A ​conical vessel, with base radius $5$ ​cm and height $24$ cm, is full of water. This ​water ​is emptied into ​a cylindrical vessel of base radius $10$ cm. Find the height to which the water will rise in the ​cylindrical vessel. ​(Use $\pi =\frac{22}{7}$)
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   The water rises to a height of $H=2$ cm in the cylinder.

   Step-by-step solution →
10. Q350 CBSE 2016
    In Fig. 5, is a decorative block, made up of two solids ​- ​a cube and a hemisphere. The base of the block is a cube of side $6$ cm and the hemisphere fixed on the ​top has a diameter ​of $3.5$ ​cm. Find ​the ​total surface area of the block. $\left(\text{use }\pi =\frac{22}{7}\right)$

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    The total surface area of the block is $225.625{\text{ cm}}^2$.

    Step-by-step solution →
11. Q351 CBSE 2016
    A hemispherical tank, ​of diameter $3$ m, is full of water. It ​is being emptied ​by a pipe at the rate ​of $3\frac{4}{7}$ litre per ​second. How much time will it take to make ​the tank half ​empty? $\left[\text{Use }\pi =\frac{22}{7}\right]$
    Show answer

    It will take $990$ seconds, that is $16$ minutes $30$ seconds, to make the tank half empty.

    Step-by-step solution →
12. Q352 CBSE 2016
    In Fig. ​5, a ​tent is in the shape of a cylinder surmounted by a ​conical ​top of same diameter. If the height and diameter of cylindrical part are $2.1$ m and $3$ m respectively and the slant height of conical part is $2.8$ m, find the ​cost of canvas needed to make the tent if the canvas is available at ​the rate of ₹$500$/sq.metre. (Use $\pi =\frac{22}{7}$.)

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    Canvas area $=33$ m${}^2$; cost $=33\times 500=$ ₹$16,500$.

    Step-by-step solution →
13. Q353 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.

    Step-by-step solution →
14. Q354 CBSE 2016
    In fig. 5, a tent is in the shape ​of ​a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are $2.1$ m and $3$ m respectively and the slant height ​of conical part is $2.8$ m, find the cost of ​canvas needed to make the tent if the ​canvas ​is available at the rate of $\text{₹}500$/sq.metre. (Use $\pi =\frac{22}{7}$)

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    Canvas area $=33$ m²; cost $=\text{₹}16500$.

    Step-by-step solution →
15. Q355 CBSE 2016
    A ​toy is in the form of a cone of radius $4.2$ ​cm mounted on a ​hemi-sphere of same radius. The total height of ​the toy ​is $9.8$ cm. Find the total ​surface ​area of ​the toy. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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    The total surface area of the toy is $203.28{\text{ cm}}^2$.

    Step-by-step solution →
16. Q356 CBSE 2016
    In Fig. 5, a tent is in the shape of a ​cylinder surmounted by ​a conical top of ​same diameter. If the height and diameter ​of cylindrical part ​are $2.1$ m and $3$ m ​respectively and the slant height ​of conical part is $2.8$ m, find the cost of canvas needed to make the tent if the canvas is ​available at the rate of $\text{₹}500$/sq.metre. (Use $\pi =\frac{22}{7}$)

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    Canvas needed $=33$ m${}^2$; cost $=\text{₹}16500$.

    Step-by-step solution →
17. Q357 CBSE 2016
    A solid iron pole consists of a cylinder of height $210$ cm and base diameter $30$ cm, which is surmounted by another solid cylinder of height $56$ cm and radius $10$ ​cm. ​Find ​the ​mass of ​the pole, given that $1{\text{ cm}}^3$ of iron has a mass of $10$ ​g. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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    The mass of the pole is $1661000$ g $=1661$ kg.

    Step-by-step solution →
18. Q358 CBSE 2016
    A cylindrical tub, whose diameter is $12$ ​cm and ​height $15$ cm is full of ice-cream. The whole ice-cream is ​to be divided into $10$ children in equal ice-cream cones, with conical ​base surmounted by hemispherical top. ​If the height of ​conical portion is twice the diameter of base, ​find the diameter of conical part of ice-cream ​cone.
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    The diameter of the conical part of each ice-cream cone is $6$ cm.

    Step-by-step solution →
19. Q359 CBSE 2016
    A 21 ​m deep well ​with diameter 6 ​m is dug and the earth from digging is evenly spread out ​to form a platform ​18 m $\times$ 11 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 $h=3$ m.

    Step-by-step solution →
20. Q360 CBSE 2016
    A conical vessel, with ​base radius $5$ cm and height $24$ cm, ​is full of water. This water is ​emptied into a cylindrical vessel of base radius $10$ cm. Find the ​height to which ​the water will rise in the cylindrical ​vessel. (Use $\pi =\frac{22}{7}$.)
    Show answer

    The water rises to a height of $2$ cm in the cylindrical vessel.

    Step-by-step solution →