Question

14. Total surface area of the cuboid is 198cm2. If the dimensisons of the cuboid are in the ratio
3:2:1 then find the length of the cuboid.​

Answer 1

Check it out ! Hope it will hep u !

Answer 2

Step-by-step explanation:

Given :-

Total surface area of the cuboid is 198cm². The dimensisons of the cuboid are in the ratio is 3:2:1.

To find :-

Find the length of the cuboid ?

Solution :-

Given that :

The ratio of the dimensions of the cuboid = 3:2:1

Let they be 3X cm , 2X cm and X cm

Length of the cuboid = 3X cm

Breadth of the cuboid = 2X cm

Height of the cuboid = X cm

We know that

Total Surface Area of a cuboid =(TSA) = 2(lb+bh+hl) sq.units

Where,

l = length

b = breadth

h = height

Now , On Substituting these values in the above formula then

=> TSA = 2[(3X×2X)+(2X×X)+(X×3X)] cm²

=> TSA = 2(6X²+2X²+3X²) cm²

=> TSA = 2(11X²) cm²

=> TSA = 22 X² cm²

Total Surface Area of the cuboid = 22 X² cm²

According to the given problem

Total surface area of the cuboid = 198cm²

=> 22 X² = 198

=> X² = 198/22

=> X² = 9

=> X =±√9

=> X = ±3

Since X is the length of the side ,It cannot be negative.

So, X = 3 cm

Now ,

3X = 3×3 cm = 9 cm

2X = 2×3 cm = 6 cm

So , length = 9 cm

Answer:-

The length of the given cuboid is 9 cm

Used formulae:-

• Total Surface Area of a cuboid =(TSA) = 2(lb+bh+hl) sq.units
• Where,
• l = length

• b = breadth

• h = height

Points to know :-

• The length of the diagonal of a cuboid = √(l²+b²+h²) units

• Curved Surface Area of a cuboid = 2h(l+b) sq.units

• Volume of a cuboid = lbh cubic units