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Question
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is
Options
27 cm2
32 cm2
44 cm2
88 cm2
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Solution
Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.
So we can take,
(l) = 3x cm
(b) = 2 x cm
(h) = x cm
We need to find the total surface area of the box
Volume of the box,
`V= 48 cm^3`
lbh = 48
(3x)(2x)x = 48
6x3 = 48
x3 = 8
x = 2
Thus,
Surface area of the box,
= 2 (lb+bh+hl)
= 2 [(3x)(2x)+(2x) x +(x)(3x)]
= 2 (11x2)
= 22 x2
= 22 (2)^2
= 88 cm2
Thus total surface area of the box is 88 cm2 .
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