Question

The volume of cuboid is 1280m^3 . its breadth and height are in ratio 5:4 and length is 16 m. find (i) the breadth (ii) the height (iii)the total surface area
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Answer 1

Given:

• The volume of cuboid is 1280 m³.

• Its breadth and height are in ratio 5:4.

• Length is 16 m.

To calculate:

• Breadth

• Height

• T.S.A

Formula used:

• Volume of the cuboid = l × b × h cubic units

• T.S.A of the cuboid = 2 ( lb + lh + bh ) sq. units

Calculation:

Let us assume the breadth and the height of the cuboid as 5x and 4x.

Calculating breadth :

As we know that,

→ Volume of cuboid = l × b × h

According to the question:

→ 1280 = 16 × 5x × 4x

→ 1280 = 16 m × 20x²

→ $\sf{ \dfrac{ 1280 }{16} }$ = 20x²

→ 80 = 20x²

→ $\sf{\dfrac{ 80 }{20 } }$ = (x²)

→ 4 = x²

→ √4 = x

→ 2 = x

Therefore,

• Breadth = 5x m

→ Breadth = 5(2) m

→ Breadth = 10 m

$\implies$ $\bf \red { Breadth = 10 \: m }$

Calculating height:

• Height = 4x m

→ Height = 4(2) m

→ Height = 8 m

$\implies$ $\bf \red { Height = 8 \: m }$

Calculating T.S.A :

→ T.S.A of the cuboid = 2 ( lb + lh + bh ) sq. units

Substituting the values of height, length and breadth we got previously.

→ T.S.A = 2 [( 16 × 10 ) + ( 16 × 8 ) + ( 10 × 8 )] m²

→ T.S.A = 2 [160 + 128 + 80 ] m²

→ T.S.A = 2 [368] m²

→ T.S.A = 736 m²

$\implies$ $\bf \red { {T.S.A}_{(Cuboid)} = 736 \: {m}^{2} }$

Answer 2

Given :-

The volume of cuboid is 1280m^3 . its breadth and height are in ratio 5:4 and length is 16 m. find

• (i) the breadth
• (ii) the height
• (iii)the total surface area

Solution :-

• (I) The Breadth is 10m.
• (II) The Height is 8m.
• (III) The Total surface area is 736m²

For More Information :-

• The Explanation is done in Attached Pic.