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Question
The length, breadth, and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm2, find dimensions of the solid.
Solution
Let the Length, breadth, and height of the cuboid be 5x,4xand 2x respectively.
Total Surface Area(TSA) = (LB+BH+LH) =1216
⇒ (LB+BH+LH) = 608
⇒ [(5x × 4x) +(4x × 2x) +(5x × 2x) =608
⇒ [20x2 +8x2+10x2] =608
⇒ 38x2 = 608
⇒ x2 = `608/38`
⇒ x2 = 16
⇒ x = 4
The dimension of the cuboid is:
Length = 5x = 5(4) = 20cm
Breadth = 4x = 4(4) = 16cm
Height = 2x = 2(4) = 8cm
∴volume = (L×B×H)
⇒ Volume = 20 × 16 × 8
⇒ Volume = 2560cm2
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