The volume of a certain rectangular solid is 8 cm^3. Its total surface area is 32 cm^2 and its three dimensions are in geometric progression. -Maths 9th

The volume of a certain rectangular solid is 8 cm^3. Its total surface area is 32 cm^2 and its three dimensions are in geometric progression. -Maths 9th
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Answer :

(b) 32 Let the edges of the solid be a, ar, ar2. Then,  Volume = a x ar x ar2 = a3r3 = (ar)3.  Given (ar)3 = 8 ⇒ ar = 2  Also, surface area = 2(a x ar + ar x ar2 + a × ar2)  = 2(a2r + a2r3 + a2r2)  = 2ar (a + ar + ar2)  Given, 2ar (a + ar + ar2) = 32  ⇒ 4(a + ar + ar2) = 32  ; Sum of lengths of all edges = 32.
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Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

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Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

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