Question

The Dimensions of a cuboid are in the ratio 4:2:1 and the total surface area is 2800m square. Find its volume.

Answer 1

Answer:

Here is your solution

Step-by-step explanation:

Let the dimensions be 4x,2x and x

Therfore, TSA of cuboid=

2(lb+bh+lh)

or 2(4x*2x+2x*x+x*4x)

or 2(8x²+2x²+4x²)

or 2(14x²)

or 28x²

But TSA=2800(Given)

So on comparing,

28x²=2800

or x²=100

or x=10

Therefore

l=40m

b=20m

h=10m

So volume=

length*breadth*height

or 40*20*10

or 8000m³

                                       

Answer 2

Let the dimensions be 4x, 2x, x

Now, Length = 2x
Breadth = x
Height = 4x

Total Surface Area = 2800

According to formula,

T.S.A =
$2(lb + bh + lh) \\ = \: 2(2x \times x + x \times 4x + 4x \times 2x) \\ = \: 2( {2x}^{2} + {4x}^{2} + {8x}^{2} ) \\ = \: 2 \times {14x}^{2} \\ now \: 2800 = 2 \times {14x}^{2} \\ or \: {x}^{2} = \frac{2800}{28} \\ or \: {x}^{2} = 100 \\ or \: x = \sqrt{100} \\ or \: x = \sqrt{10 \times 10} \\ or \: x = 10$
Now length = 2x = 2× 10
= 20 m
Breadth = x = 10 m
and Height = 4x = 4×10= 40 m
Now volume = l×b×h
= (20×10×40) m^3
= 8000 m^3