Question

the volume of a cubiod is 1280mcube. its breadth and height are in the ratio of 5:4and length is 16 m. find (1) the breadth (2)the height (3)the total surface area

Answer 1

It is given that the volume of cuboid is 1280 m³ and the ratio of breadth and height is in the ratio of 5 : 4. Also, the length of the cuboid is 16 m.


Let the breadth of the cuboid be 5 a and the height of the cuboid be 4 a, where a is a constant.



From the properties of cuboid, we know : -

Volume of cuboid = length x breadth x height



Therefore,

= > 1280 = 16 m x 4 a x 5 a

= > 1280 m³ / 16 m = 20 a²

= > 80 m² = 20a²

= > 80 / 20 m² = a²

= > 4 m² = a²

= > 2 m = a



Hence,
value of assumed constant variable ( i.e. a ) is 2 m.


( 1 ) : Breadth


From above,
Breadth of the cuboid = 5 a = 5( 2 m ) = 10 m


Hence,
Breadth of the cuboid is 10 m



( 2 ) : Height of the cuboid = 4 a = 4( 2 m ) = 8 m


Thus,
Height of the cuboid is 8 m.


( 3 ) : TSA


From the properties of cuboid, we know : -

TSA of cuboid = 2( lb + bh + hl ), where I is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.


Now,

TSA of cuboid = 2[ ( 16 x 5a ) + ( 5a x 4a ) + ( 4a x 16 ) ]


TSA = 2[ 80a + 20a² + 64a ] m²

TSA = 2[ 80(2) + 20(2) + 64(2) ] m²

TSA = 2[ 160 + 40 + 128 ] m²

TSA = 2[ 328 m² ]

TSA = 656 m²


Hence,
Total surface area of the cuboid is 656 m².
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