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Question
The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
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Solution
Surface area of cuboid = 2548 cm2
Ratio in length, breadth and height of a cuboid = 4 : 3 : 2
Let length = 4x, Breadth = 3x and height = 2x
`therefore "Surface area" = 2(4x xx 3x + 3x xx 2x + 2x xx 4x)`
= `2(12x^2 + 6x^2 + 8x^2)`
= `2 xx 26x^2 = 52x^2`
`therefore 52x^2 = 2548`
`x^2 = 2548/52 = 49 = (7)^2`
`therefore x = 7`
`therefore "Length" = 4x = 4 xx 7 = 28` cm
`therefore "Breadth" = 3x = 3 xx 7 = 21` cm
`"and height" = 2x = 2 xx 7 = 14`cm
`therefore "Volume" = lbh`
`= 28 xx 21 xx 14` cm3 = 8232 cm2
(ii) If volume = 3000 m3
⇒ `4x xx 3x xx 2x = 3000`
⇒ `24x^3 = 3000`
⇒ `x^3 = 3000/24 = 125 = (5)^3`
`therefore x = 5`m
`"Length" = 5 xx 4 = 20, "breadth" = 5 xx 3 = 15`m
and height = `5 xx 2 = 10`m
`therefore "Surface area" = 2[lb + bh + hl]`
= `2[20 xx 15 + 15 xx 10 + 10 xx 20]`m2
= `2[300 + 150 + 200]`m2
= `2 xx 650 = 1300`m2
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