The dimensions of cuboid are in ratio 3:2:1 and total surface area is 2,8,16 square cm .Find its volume?
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Given that
Dimensions of a cube are in the ratio = 3:2:1
Total surface area = 2,816 cm^2
Solution
Let the dimensions of the cuboid 3x , 2x and x. Then,
according to question,
Total surface area of the cuboid
= 2 (lb + lh + bh)
= 2 (3x × 2x + 3x × x + 2x × x)
= 2 (6x^2 + 3x^2 + 2x^2)
= 2 (11x^2)
= 22x^2
Therefore , 22x^2 = 2,816
=> x^2 = 2,816/22
=> x^2 = 128
=> x = √128
=> x = 11.3
Hence ,
Length of a cuboid = 3 × 11.3 = 33.9 cm
Breadth of a cuboid = 2 × 11.3 = 22.6 cm
Height of a cuboid = 11.3 cm
Volume of a cuboid = length × breadth × height
= (33.9 × 22.6 × 11.3) cm^3
= 8,672.382 cm^3
Thanks
Given that
Dimensions of a cube are in the ratio = 3:2:1
Total surface area = 2,816 cm^2
Solution
Let the dimensions of the cuboid 3x , 2x and x. Then,
according to question,
Total surface area of the cuboid
= 2 (lb + lh + bh)
= 2 (3x × 2x + 3x × x + 2x × x)
= 2 (6x^2 + 3x^2 + 2x^2)
= 2 (11x^2)
= 22x^2
Therefore , 22x^2 = 2,816
=> x^2 = 2,816/22
=> x^2 = 128
=> x = √128
=> x = 11.3
Hence ,
Length of a cuboid = 3 × 11.3 = 33.9 cm
Breadth of a cuboid = 2 × 11.3 = 22.6 cm
Height of a cuboid = 11.3 cm
Volume of a cuboid = length × breadth × height
= (33.9 × 22.6 × 11.3) cm^3
= 8,672.382 cm^3
Thanks
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0
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