Question

The dimensions of a cuboid are in the ratio 1 : 2 : 3 , and its TSA is 88m2 . Find its volume.

Answer 1

☣Let the dimensions be x

so :- 1x , 2x , 3x are respectively length, breadth and height of cuboid

TSA of cuboid =
$= 2(lb \: + bh + hl)$

88 = 2 { ( x × 2x) + (2x × 3x) + (3x × x) }

44 = 2x² + 6x² + 3x²

44 = 11x²

4 = x²

√4 = x

2 = x

⭐ So,

☣ length ( l ) = x = 2m

☣ Breadth ( b ) = 2x = 2×2 = 4m

☣ Height ( h ) = 3x = 3 × 2 = 6m

☢ Volume of Cuboid = l × b × h

= 2 × 4 × 6

= 48m³

So,

➡ the volume of cuboid = 48m²

@Altaf

Answer 2

Hello.............. ^_^

Here is your answer......

Given :-
dimensions of a cuboid are in ratio 1:2:3
total surface area is 88m square.

let,
length be 3x m
breath be 2x m
height be 1x m

$total \: \: surface \: \: area = 88 {m}^{2} \\ \\ = > 2(length \times breadth + breadth \times height + height \times length) = 88 \\ \\ = > 2(3x \times 2x + 2x \times 1x + 1x \times 3x) = 88 \\ \\ = > 2(6 {x }^{2} + 2 {x}^{2} + 3 {x}^{2} ) = 88 \\ \\ = > 2(11 {x}^{2} ) = 88 \\ \\ = > 11 {x}^{2} = \frac{88}{2 } \\ \\ (88 \div 2 = 44) \\ \\ = > 11 {x }^{2} = 44 \\ \\ = > {x}^{2} = \frac{44}{11} \\ \\ (44 \div 11 = 4) \\ \\ = > {x}^{2} = 4 \\ \\ = > x = \sqrt{4 } \\ \\ = > x = 2$

length = 3x = 3 X 2 = 6m
breadth = 2x = 2 X 2 = 4m
height = 1x = 1 X 2 = 2m


Volume of cuboid = length X breadth X height
$= 6 \times 4 \times 2 \: \: {m}^{3} \\ = 48 {m}^{3}$


Hope it helps............... ^_^