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NCERT Exemplar · Class 10 Mathematics Surface Areas and Volumes

62 questions · 62 still being checked

EXERCISE 12.3 11–14 (part 5 of 7)

  1. Exercise 11

    How many spherical lead shots each of diameter 4.2\displaystyle 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66\displaystyle 66 cm, 42\displaystyle 42 cm and 21\displaystyle 21 cm.

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    NCERT’s answer
    $\displaystyle 1500$
    The count is the cuboid's volume divided by one shot's volume: \[V_{\text{cuboid}} = 66\times 42\times 21 = 58212 \text{ cm}^3 \] \[V_{\text{shot}} = \frac{4}{3}\pi (2.1)^3 = \frac{4}{3}\pi (9.261) \text{ cm}^3 \] \[n = \frac{58212}{\dfrac{4}{3}\pi(9.261)} = 1500 \] Answer: $\displaystyle 1500$ lead shots.

  2. Exercise 12

    How many spherical lead shots of diameter 4\displaystyle 4 cm can be made out of a solid cube of lead whose edge measures 44\displaystyle 44 cm.

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    NCERT’s answer
    $\displaystyle 2541$
    The cube's volume divided by one shot's volume gives the count: \[V_{\text{cube}} = (44)^3 = 85184 \text{ cm}^3 \] \[V_{\text{shot}} = \frac{4}{3}\pi (2)^3 = \frac{32\pi}{3} \text{ cm}^3 \] \[n = \frac{85184}{\dfrac{32\pi}{3}} = 2541 \] Answer: $\displaystyle 2541$ lead shots.

  3. Exercise 13

    A wall 24\displaystyle 24 m long, 0.4\displaystyle 0.4 m thick and 6\displaystyle 6 m high is constructed with the bricks each of dimensions 25 cm×16 cm×10 cm\displaystyle 25 \mathrm{~cm} \times 16 \mathrm{~cm} \times 10 \mathrm{~cm}. If the mortar occupies 110\displaystyle \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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    NCERT’s answer
    $\displaystyle 12960$
    Mortar takes \(\displaystyle \frac{1}{10}\) of the wall's volume, so bricks fill \(\displaystyle \frac{9}{10}\): \[V_{\text{wall}} = 24\times 0.4\times 6 = 57.6 \text{ m}^3 = 57{,}600{,}000 \text{ cm}^3 \] \[V_{\text{bricks}} = \frac{9}{10}\times 57{,}600{,}000 = 51{,}840{,}000 \text{ cm}^3 \] \[V_{\text{brick}} = 25\times 16\times 10 = 4000 \text{ cm}^3 \] \[n = \frac{51{,}840{,}000}{4000} = 12{,}960 \] Answer: $\displaystyle 12,960$ bricks.

  4. Exercise 14

    Find the number of metallic circular disc with 1.5\displaystyle 1.5 cm base diameter and of height 0.2\displaystyle 0.2 cm to be melted to form a right circular cylinder of height 10\displaystyle 10 cm and diameter 4.5\displaystyle 4.5 cm.

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    NCERT’s answer
    $\displaystyle 450$
    Melting conserves volume, the discs' total equals the cylinder's: \[V_{\text{disc}} = \pi (0.75)^2(0.2) = 0.1125\pi \text{ cm}^3 \] \[V_{\text{cylinder}} = \pi (2.25)^2(10) = 50.625\pi \text{ cm}^3 \] \[n = \frac{V_{\text{cylinder}}}{V_{\text{disc}}} = \frac{50.625}{0.1125} = 450 \] Answer: $\displaystyle 450$ discs.