Question

the dimension of a cuboid are in ratio 5 ratio 2 ratio its volume is 1 and 1250 cubic metres what is the total surface area

Answer 1

$area \: of \: a \: cuboid = 5x \times 2x \times x = 1250$
or,
$10x3 = 1250$
or,
$x3 = 1250 \div 10 = 125$
or,
$x = \sqrt[3]{125}$
or,
$x = \sqrt[3]{5 \times 5 \times 5}$
or,
$x = 5$
so, dimension of cuboid=
$25 \times 10 \times 5$
so total surface area=
$2({lb + bh + lh})$
$= 2 \times ( {25 \times 10 + 10 \times 5 + 25 \times 5})$
$2 \times (250 + 50 + 125)$
$= 2 \times 425$
$= 850 {m}^{2}$
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Answer 2

Correct Question:

The dimension of a cuboid are in the ratio 5:2:1 .Its volume is 1250 cubic metres. What is the total surface area?

Solution :

Let,

Length=5x

Breadth=2x

Height=x

Now,

L×B×H=1250

5x*2x*x=1250

x³=125

x=5m

Replacing x with 5

L=5×5=25m

B=5×2=10m

H=5m

Replacing area: 2(lb+bh+hl)

2(25×10+10×5+25×5)

2(250+50+125)

2(425)=850m³

Therefore,

The total surface area is 850m³