The length breath and height of a rectangular soild are in the ratio of 5:4:2 if its total surface area is 1216 cm²,find the volume of the solid ?
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The length, breadth and height of a rectangular solid are in the ratio 5:4:2. If the total surface area is 1216 cm
2
, find the length of solid in cm.
Answer
The rectangular solid is a cuboid.
Let the length of the cuboid =5a, breadth =4a, and height =2a
Total surface area of a cuboid of length l, breadth b and height h =2(l×b+b×h+l×h)
Given, total surface area of the cuboid =1216cm
2
⇒2(5a×4a+4a×2a+2a×5a)=1216cm
2
⇒76a
2
=1216
⇒a=4
Hence, the length of the cuboid =5a=20 cm, breadth =4a=16 cm, height =2a=8 cm
The rectangular solid is a cuboid.
Let the length of the cuboid =5a, breadth =4a, and height =2a
Total surface area of a cuboid of length l, breadth b and height h =2(l×b+b×h+l×h)
Given, total surface area of the cuboid =1216cm2
⇒2(5a×4a+4a×2a+2a×5a)=1216cm2
⇒76a2=1216
⇒a=4
Hence, the length of the cuboid =5a=20 cm, breadth =4a=16 cm, height =2a=8 cm
Volume of a cuboid = lbh
20*16*8
= 2560 cm^3
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