h
y
X
Based on the above information answer the following
(i) If x, y and h represent the sides of the base and height of the tank respectively then area A of metal sheet
used is
(a) 2(x+y) x h=A
(b) (2x+ y) x h =A
(c)x+y +h=A
(d) x2 + 4xh = A
(ii) The volume of water is
ontheyan
To conserve water for emergency needs in a village, the Gram Panchyat decides to construct an open tank
with a square base from a metal sheet which has been donated by a company, from the account of social
welfare account. The area of metal sheet donated is to be least and water to be stored is 4000 m.
Answers
Given : an open tank with a square base from a metal sheet
he area of metal sheet donated is to be least and water to be stored is 4000 m.
To Find : x, y and h represent the sides of the base and height of the tank respectively then area A of metal sheet used is
Area of Sheet Metal
Solution:
area of metal sheet used A = xy + 2(x + y) h ( as open from Top)
as square base hence y = x
A = x² + 2(x + x) h
A = x² + 4xh
A = x² + 4xh
V = x²h
V = 4000
=> h = 4000/x²
A = x² + 4x (4000/x²)
=> A = x² +16000/x
=> dA/dx = 2x - 16000/x²
dA/dx = 0
=> 2x - 16000/x² = 0
=> x³ = 8000
=> x = 20
d²A/dx² = 2 + 32000/x³ > 0 Hence Area is least
x = 20 => h = 4000/x² = 10
Area of metal sheet = x² + 4xh
= 400 + 4*20 * 10
= 1200 m²
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