Question

The dimensions of pool are in the ratio 1:3:4 if its volume 6144m^3. Find the total surface area of the pool Answer is 1664m^2 please give answer in step-by-step​

Answer 1

The surface area of cuboid is 2432 sq.m.

Step-by-step explanation:

The dimensions of pool are in the ratio 1:3:4

Let the ratio be x

Length = x

Breadth = 3x

Height = 4x

Volume of pool =  

Volume of pool =  

We are given that the volume of pool is 6144 cubic m

So,

Length = 8 m

Breadth = 3(8)=24

Height=4(8)=32

Total surface area of cuboid =  

Hence the surface area of cuboid is 2432 sq.m.

#Learn more:

If a cube has a surface area of 6144m², then find  the volume of the cube.​

brainly.in/question/12178232

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The dimensions of pool are in the ratio 1:3:4.

So, Let assume that

Length of cuboid = x m

Breadth of cuboid = 3x m

Height of the cuboid = 4x m

Further given that

$\rm \: Volume_{(cuboid)} \: = \: 6144 \: {m}^{3}$

We know,

Volume of cuboid of length (l), breadth (b) and height (h) is given by

$\boxed{\sf{  \:\rm \: Volume_{(cuboid)} \: = \: l \: \times \: b \: \times \: h \: \: }}$

So, on substituting the values, we get

$\rm \: x \times 3x \times 4x = 6144$

$\rm \: {12x}^{3} = 6144$

$\rm \: {x}^{3} = 512$

$\rm \: {x}^{3} = {8}^{3}$

$\rm\implies \:x = 8 \:$

Thus,

Length of cuboid = 8 m

Breadth of cuboid = 3 × 8 = 24 m

Height of the cuboid = 4 × 8 = 32 m

Now, We know Total Surface Area (TSA) of cuboid of length (l), breadth (b) and height (h) is given by

$\boxed{\sf{  \:\rm \: TSA_{(cuboid)} = 2(lb + bh + hl) \: \: }}$

So, on substituting the values, we get

$\rm \: TSA_{(cuboid)} = 2(8 \times 24 + 24 \times 32 + 32 \times 8)$

$\rm \: =  \:2(192 + 768 + 256)$

$\rm \: =  \:2 \times 1216$

$\rm \: =  \:2432 \: {m}^{2}$

Hence,

$\rm\implies \:\boxed{\sf{  \:\rm \: TSA_{(cuboid)} \: = \: 2432 \: {m}^{2} \: \: }}$

$\rule{190pt}{2pt}$

Additional Information

Formulae of Cube :-

Total Surface Area = 6(side)²

Curved Surface Area = 4(side)²

Volume of Cube = (side)³

Diagonal of a cube = √3(side)

Perimeter of cube = 12 x side

Formulae of Cuboid

Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

Curved Surface area = 2 height(length + breadth)

Volume of the cuboid = (length × breadth × height)

Diagonal of the cuboid =√(l² + b² + h²)

Perimeter of cuboid = 4 (length + breadth + height)