Question

the total surface area of a cuboid is 214 sq.cm . its length is 7 cm and breadth is 6 cm . Find its volume.​

Answer 1

Given:

• The Total Surface Area(TSA) of a cuboid is 214 cm sq.
• The length (l) of the cuboid is 7 cm
• The breadth (b) of the cuboid is 6 cm

To find:

The volume of the cuboid

The formula to find the volume of the cuboid is

= lbh unit cube.

[Here, 'l' is the 'length', 'b' is the 'breadth', and 'h' is the 'height' of the cuboid]

So,

We have length and breadth, we need height of the cuboid.

We can find the height of the cuboid by the TSA formula

The formula to find the Total Surface Area of a cuboid is

= 2(lb+bh+hl) unit sq.

So,

⇒ 2 [ (7*6) + (6*h) + (h*7) ] = 214

⇒ 2[ 42 + 6h + 7h ] = 214

⇒ 2 [42 + 13h] = 214

⇒ 42 + 13h = 214 ÷ 2

⇒ 42 + 13h = 107

⇒ 13h = 107 - 42

⇒ 13h = 65

⇒ h = 5

∴The height of the cuboid is 5 cm

Now

• The volume of the cuboid is

= lbh

= 7*6*5

= 210 cm ³

Hence,

The volume of the cuboid is 210 cm cube.

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More Information:

• Lateral/Curved Surface Area of cuboid = 2h( l+b ) unit sq.

Answer 2

Answer:

210 cm cube

Step-by-step explanation:

Total surface area = 214 cm sq. (given)

Length = 7 cm and breadth = 6 cm (given)

So,

2(lb+bh+hl) = 214

→ 2(7×6 + 6×h + h×7) = 214

→ 2( 42 + 6h + 7h ) = 214

→ 2 (42 + 13h) = 214

→ 42 + 13h = 214 ÷ 2

→ 42 + 13h = 107

→ 13h = 107 - 42

→ 13h = 65

→ h = 5

And

Volume of the cuboid = lbh

= 7×6×5 = 210 cm cube