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1 Let its height be 12x and its width be 5x

2 If: (2*12x*5x)+(2*12x*30)+(2*30) = 2520 sq cm

3 Then: 120x2+720x+300x = 2520

4 And so: 120x2+1020x = 2520 => 120x2+1020x-2520 = 0

5 Solving the above quadratic equation gives x a positive value of 2

6 Therefore: height is 12*2 = 24 cm and width is 5*2 = 10 cm

7 Volume: 24*10*30 = 7200 cubic cm

8 Check: (2*24*10)+(2*24*30)+(2*10*30) = 2520 square cm

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Q: What is the volume of a cuboid when its height is in the ratio of 12 to 5 to its width and has a length of 30 cm with a surface area of 2520 square cm showing all work?
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