Question

The dimensions of a cuboid are in the ratio 4:3:2 . if the total surface area of a cuboid is 4212sqm,find the dimensions of the cuboid

Answer 1

Given :-

Total surface area of cuboid = 4212 $m^2$

Ratios of dimension of a cuboid = 4:3:2

Dimensions of a cuboid = length, breadth, height

So,

Let the length = 4x

Breadth = 3x

Height = 2x

To find :-

The dimensions of a cuboid = ?

Solution :-

As we know,

Total surface area = 2( lb + bh + lh)

Put the given values,

$2(4x \times 3x + 3x \times 2x + 2x \times 4x) = 4212$

$2(12x^2 + 6x^2 + 8x^2) = 4212$

$2(26 {x}^{2} ) = 4212$

$52 {x}^{2} = 4212$

$x^2 = \dfrac{4212}{52}$

${x}^{2} = 81$

$x = \sqrt{81}$

$x = \sqrt{9 \times 9}$

$x = 9$

The value of x = 9

Let the length = 4x = 4 × 9 = 36m

Breadth = 3x = 3 × 9 = 27m

Height = 2x = 2 × 9 = 18m

_______________

Additional Information :-

▪ Volume of cube = side × side × side

▪ Diagonal of cube = $\sqrt{3l}$

▪Perimeter of cube = 12 × side

▪ Volume of cuboid = length × breadth × height

▪ Diagonal of cuboid = $\sqrt{( l^2 + b^2 + h^2})$

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

Answer 2

Answer:

Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs

Step-by-step explanation:

Pʟs ᴍᴀʀᴋ ᴀs ʙʀᴀɪɴʟɪᴀsᴛ ᴀɴᴅ ғᴏʟʟᴏᴡ ᴍᴇ✌️