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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
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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