The dimensions of a cuboid are in the ratio 6:2:3 . It's volume is 2.304 m cube. Find the dimensions and hence total surface area of cuboid
Answers
l=6xm , b=2xm, h=3xm
volume = lbh
2.304=6x×2x×3x
2.304=36x^3
0.064=x^3
x= 0.4m
l= 2.4 m
b=0.8m
h=1.2m
T.S.A = 2(lb+bh+hl)
= 2(2.4×0.8+0.8×1.2+1.2×2.4)
=2×5.76 =11.52 m^2
Dimension = 2.4 m* 0.8 m * 1.2 m , Total Surface area = 11.52 m²
Step-by-step explanation:
The dimensions of a cuboid are in the ratio 6:2:3
Let say Dimension of cuboids are
6L , 2L & 3L cm
Volume = 6L * 2L * 3L = 36 L³ cm³
volume is 2.304 m³ = 2.304 * 10⁶ cm³
36 L³ = 2.304 * 10⁶ cm³
=> 36 L³ = 2304 * 10³ cm³
=> L³ = 64 * 10³ cm³
=> L³ = 4³ * 10³ cm³
=> L = 4 * 10 = 40 cm
6L = 6 * 40 = 240cm = 2.4 m
2L = 2 * 40 = 80 cm = 0.8 m
3L = 3 * 40 = 120 cm = 1.2 m
Dimension = 2.4 m * 0.8 m * 1.2 m
Total Surface area = 2 ( 2.4 * 0.8 + 2.4 * 1.2 + 0.8*1.2)
= 2(1.92 + 2.88 + 0.96)
= 2 ( 5.76)
= 11.52 m²
Total Surface area = 11.52 m²
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