Question

The length, breadth and height of a rectangular box are as 1:2:3. Find the volume of the box,when its surface area is 1078 m square

Answer 1

Let length, breadth and height be
L = y, B = 2y and H = 3y respectively
Given,
2×(LB+LH+BH) = 1078
2×(y × 2y + y × 3y + 2y × 3y) = 1078
2×11y² = 1078
y = 7

Thus, L = 7 m, B = 14 m, H = 21 m
Therefore, volume = LBH = 7×14×21 = 2058 m³

Answer 2

The Volume of the box is 2058 cubic meter.

Step-by-step explanation:

Given,

Surface Area = 1078 sq. m.

Since The length, breadth and height of a rectangular box are as 1:2:3.

therefore length = x     breadth = 2x     height = 3x

Now we use the formula of surface area.

$surface\ area = 2(length\times breadth+breadth\times height+height\times length)$

On putting the values, we get;

$2(x\times2x+2x\times3x+3x\times x)=1078\\\\2(2x^2+6x^2+3x^2)=1078\\\\2\times11x^2=1078\\\\11x^2=\frac{1078}{2}=539\\\\x^2=\frac{539}{11}=49\\\\x=\sqrt{49}=7\ m$

So, $length=7 m$

$breadth = 2x=2\times7=14\ m$

$height = 3x=3\times7=21\ m$

We have to find out the volume of the box.

$Volume= length\times breadth\times height$

$volume = 7\times14\times21=2058\ m^3$

Hence The Volume of the box is 2058 cubic meter.