Chapter 12 · Surface Areas and Volumes

NCERT Exemplar Class 10 Maths Exercise 12.3

All 14 questions of NCERT Exemplar Class 10 Maths Exercise 12.3 (Surface Areas and Volumes), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Three metallic ​solid cubes whose edges ​are 3 cm, 4 cm ​and 5 cm are ​melted ​and formed into ​a single cube. Find the ​edge of the cube so formed.
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   The edge of the cube formed is $6$ cm.

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2. Q2
   How many ​shots ​each having diameter 3 cm can be ​made from ​a ​cuboidal lead ​solid ​of ​dimensions $9\text{ cm}\times 11\text{ cm}\times 12\text{ cm}$?
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   $84$ spherical lead shots can be made.

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3. Q3
   A ​bucket is in the form of a ​frustum of a cone and holds $28.490$ litres ​of ​water. The radii of the ​top and bottom are $28$ cm and $21$ cm, ​respectively. ​Find the height of the bucket.
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   The height of the bucket is $15$ cm.

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4. Q4
   A cone of radius 8 cm and height 12 cm is ​divided ​into two parts by a ​plane ​through the mid-point of its axis ​parallel ​to its base. Find the ratio ​of the volumes of two ​parts.
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   The ratio of the volumes (small cone : frustum) is $1:7$.

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5. Q5
   Two identical cubes each of volume $64{\text{cm}}^3$ are joined ​together end to end. ​What ​is ​the ​surface ​area of the ​resulting cuboid?
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   The surface area of the resulting cuboid is $160{\text{cm}}^2$.

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6. Q6
   From a solid cube ​of ​side 7 cm, ​a conical cavity of height ​7 ​cm ​and ​radius 3 cm is hollowed out. Find ​the volume of the remaining solid.
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   Volume of the remaining solid $=277$ cm${}^3$.

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7. Q7
   Two ​cones with same base ​radius 8 cm and height 15 cm are joined together along ​their bases. ​Find ​the surface area ​of the shape so formed.
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   Surface area $=\frac{5984}{7}\approx 854.86{\text{cm}}^2$.

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8. Q8
   Two solid cones A and B are placed in a cylindrical ​tube as ​shown in Fig. 12.9. The ​ratio ​of their capacities ​is 2:1. Find the heights ​and ​capacities of the ​cones. Also, find the volume of the remaining portion of the cylinder. (The cylindrical tube has length 21 cm and diameter 6 cm.)

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   Heights: $h_A=14$ cm, $h_B=7$ cm; capacities $V_A=42\pi \approx 131.9$ cm${}^3$, $V_B=21\pi \approx 66.0$ cm${}^3$; remaining volume $=126\pi \approx 395.8$ cm${}^3$.

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9. Q9
   An ice cream cone full of ice ​cream having radius ​5 cm and height 10 cm ​as shown in ​Fig. 12.10. Calculate the volume of ice cream, ​provided that its $\frac{1}{6}$ ​part is left unfilled ​with ice ​cream.

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   Volume of ice cream $=\frac{625}{6}\pi \approx 327.4{\text{cm}}^3$ (taking $\pi =\frac{22}{7}$).

   Step-by-step solution →
10. Q10
    Marbles of diameter 1.4 ​cm are ​dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number ​of marbles ​that should be ​dropped into the ​beaker so ​that the water ​level rises by 5.6 cm.
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    $150$ marbles should be dropped into the beaker.

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11. Q11
    How ​many spherical lead ​shots each of diameter 4.2 cm can be obtained from a solid ​rectangular lead ​piece with ​dimensions 66 cm, 42 ​cm and 21 cm.
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    $1500$ spherical lead shots can be obtained.

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12. Q12
    How many spherical lead shots of diameter 4 cm can be made out of ​a solid cube ​of ​lead whose ​edge ​measures ​44 ​cm?
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    $N=2541$ spherical lead shots can be made.

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13. Q13
    A wall 24 ​m long, 0.4 m thick and 6 ​m high is constructed with the bricks each ​of dimensions $25\text{ cm}\times 16\text{ cm}\times 10\text{ cm}$. If the mortar occupies $\frac{1}{10}$th of ​the volume of the wall, then ​find the number ​of bricks ​used in constructing the wall.
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    $12960$ bricks were used in constructing the wall.

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14. Q14
    Find ​the number of metallic circular discs with 1.5 cm ​base ​diameter and of height 0.2 cm to ​be melted to form a ​right ​circular cylinder of height 10 cm and diameter ​4.5 cm.
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    $n=450$ discs must be melted.

    Step-by-step solution →