The volume of a cuboid is 1280 m! Its breadth and height are in the ratio of 5 : 4 and length is
10 m. Find the breadth (ii) the height and (iii) the total surface area
Answers
Answer:
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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Answer:
Hope it helps you
Step-by-step explanation:
answer is in attatchment.
height = 4x
= 4× 2 = 8m
