Question

find the volume of cuboid if itts surface area is 208cm² abd the ratio of dimension are 2:3:4​

Answer 1

Solution:-

Given :-

• Surface area of cuboid = 208 cm²
• Ratio of dimensions = 2:3:4

Find :-

• Volume of cuboid

Explanation

Formula

$\dag\boxed{\underline{\tt{\red{\: Surface\:area_{cuboid}\:=\:2\times(LW+WH+HL)}}}}$

$\dag\boxed{\underline{\tt{\orange{\: Volume_{cuboid}\:=\:(L\times W\times H)}}}}$

Where

• L = Length
• W = Width
• H = Height

Let,

• Length be = 2x
• Width = 3x
• Height = 4x

So, Now,

==> Surface area of cuboid = 2×(2x × 3x + 3x × 4x + 4x × 2x)

==> 208 = 2×(6x² + 12x² + 8x²)

==> 52x² = 208

==> x² = 208/52

==>. x² = 4

==> x² = 2²

==> x = 2

Since

• Length will be = 2x = 2×2 = 4 cm
• Width will be = 3x = 3×2 = 6 cm
• Height will be = 4x = 4×2 = 8 cm

Now, calculate volume ,,

==> Volume of cuboid = 4×6×8

==> Volume of cuboid= 192 cm³

Hence

• Volume of required cuboid be = 192 cm³

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