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Arrange the following three-dimensional objects in the descending order of their volumes:

  1.    A cuboid with dimensions $\text{10 cm, 8 cm and 6 cm}$
  2.    A cube of side $\text{8 cm}$
  3.    A cylinder with base radius $\text{7 cm}$ and height $\text{7 cm}$
  4.    A sphere of radius $\text{7 cm}$
  1. $\text{i), ii), iii), iv)}$
  2. $\text{ii), i), iv), iii)}$
  3. $\text{iii), ii), i), iv)}$
  4. $\text{iv), iii), ii), i)}$
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Volume of each one is:

  1. $V_{\text{cuboid}} = l*b*h = 10 * 8  * 6 = 480\ cm^2$ 
  2. $V_{\text{cube}} = a^3 = 8^3 = 512\ cm^2$
  3. $V_{\text{cylinder}} = \pi r^2h \approx 1077.57\ cm^2$
  4. $V_{\text{sphere}} = \frac{4}{3} \pi r^3 \approx 1436.76\ cm^2$

So, the descending order is:

(D) (iv), (iii), (ii), (i)

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Vol of cuboid: L * B * H

                       =  10 * 8 * 6 = 480 cm3

Vol of cube: L3

                        = 83   

                        = 512 cm3

Vol of cylinder: π*h*r2

                                  = 1077.566 cm3

Vol of a sphere: 4/3*π*r3

                     = 1436.755 cm3

So, descending order is (IV), (III), (ii) and (i)

option D

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