A box made of sheet metal cost ₹2820 at the rate of ₹30 per sq m. If the box is 5 m long and 4 m wide, find its height.
Answers
Answer:
Height is 3m
Step-by-step explanation:
Area in sq meters sold in the sheet=2820/30=94
Area of rectangular base of the box=20 sq m
If the box is horizontal & h is the height,the area covered by all the 6 sheets=4h+4h+40+5h+5h=94
18h+ 40=94
18h=54
h=3
Height is 3 metres.
If the box is kept vertically,the height becomes 5 mtrs & length & breath of base and top sheets will be 4 mtrs & 3 mtrs,each.
2 example
3 M height.
Total surface area of a box=2[LH+2LB+2BH.(1), where L, B, and H are Length, Breadth, and Height respectively:
assume X M height, then total surface area per equation 1, = 2[(5*X)+(5*4)+(4*X)]…. (2)
however from the total cost and sheet metal rate, we know the total area as total cost/ cost per square meter,=2820/30=94 sq. Meters
hence equation 2=94, solving for X, we get X=3.
3 example
sheet of metal used for box=2820/30= 94 m
sheet of metal used for top and bottom of box=2*5*4=40 m
sheet of metal used for all 4 sides and height=94–40=54 m
All 4 sides=2(5+4)=18 m
Height=54/18=3 m
4 example
The total surface area of the box is 2820/30 = 94 sq.m.
If the height of the box is h , the surface area of the box is
2 × 5×4 + 2 × 5×h + 2 × 4×h. = 40 +10h + 8h = 18h+40.
Therefore 18h + 40 = 94
Or 18h = 94 - 40 = 54.
Or h = 54/18 =3 m.
Therefore height of the box is 3 meters.
5 example
Total metal used = 2820÷30
I.e. 94m
Metal used in base and top = 2×5×4
I.e. 40m
Remaining metal = 94-40
I.e. 54m
Metal used in sides of the box is = 2×(5+4) (per side)
I.e. 18m
Hence height of the box is 54÷18
I.e 3m
6 example
Total surface area of the cuboid =2(lb+bh+hl) = 2820/30= 94
here l= 5-m;
b= 4-m
h = ?
So 2(20+4h+5h)= 94
So 9h+20= 47
9h= 27- m
So h= 3- m
Therefore the height of the box = 3- m
7 example
For ₹ 30 ……………..area of metal sheet is 1 sq.m
For ₹ 2820………………………………………………………?
2820/30=94 sq.m
Total surface area of box=2(l×b+b×h+h×l)=94
2(5×4+4×h+h×5)=94
20+9h=47
9h=27
h=27/9=3 m
8 example
Total cost/ rate is area of sheet required.2820/30=94. Less top and bottom of 5x4 size is 40. Balance is 54 sq m. Total 4 sides with height h is 5xh+5xh+4xh+4xh=18h. So height is 54/18=3 mtr
9 example
Total metal used = 2820/30= 94 m
Total surface area= 2(lb+bh+lh)
2(5*4+4h+5h)=94
2(20+9h)=94
40+18h=94
h= 54/18=3 m
10 example
Area of sheet=2820/30=94 sq m
Top & bottom area = 5×4=20sq m
H=(94–20×2)/2/(5+4)=3m
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