A factory owner wants to construct a tank with rectangular base and rectangular sides, open at
the top, so that its depth is 2m and capacity is 8 3
. The building of the tank costs Rs. 280 per square
meter for the base and Rs. 180 per square meter for the sides.
Based on the above information, answer the following questions:
(i) If the length and the breadth of the rectangular base of the tank are x meters and y meters
respectively, then the relation between x and y is
(a) x +y=4 (b) x y=4 (c) x y=8 (d) x y + x +y=4
(ii) The cost of construction of the base of the tank is
(a) Rs. 180(x +y) (b) Rs. 360( x +y) (c)Rs. 720(x +y) (d) Rs. 1120(x +y)
(iii) If C (in Rs.) is the cost of construction of the tank , then C as a function of x is
(a)C=1120+720(x+4
) (b) C=720+1120(x+ 4
) (c) C=1120+360(x+ 4
) (d) C = 1120+180(x+ 4
)
(iv) The least cost of construction of the tank is (a)Rs.2000 (b)Rs.3000 (c)Rs.3600 (d)Rs.4000
please tell fast
Answers
Answer:
Step-by-step explanation:
A factory owner wants to construct
a tank with rectangular base and rectangular sides, open at
t
he top, so that its depth is 2m and capacity is 8 3
. The b
uilding of the tank costs Rs. 280 per square
meter for the base and Rs. 180 per square meter for the sides.
Based on the above information, answer the following questions:
Answer:
1.Option(b) xy=4 , 2.option(c) Rs.720(x+y), 3.Option(a)1120+720(x+4/x)
Step-by-step explanation:
Given: Depth(height) of a rectangular tank = 2m
Volume of tank =8m³
building cost for base of tank per sq.m =Rs.280
building cost for sides per sq.m=Rs. 180
To find: (1)Relation between length x and breadth y,
(2)cost of construction of base,
(3)express the cost C as the function of x
(4)least cost of construction.
Solution :Volume of cuboid = lbh
volume of cuboidal tank = 8m³
l×b×h = 8
h=2m, l×b×2 = 8
⇒ l×b = 8÷2 = 4 ------eq.(1)
(1) if length and breadth are x meters and y meters then the relation between x and y is x×y = 4 , from eq.(1)
So option (b) xy = 4 is the answer.
(2) Base area = area of rectangle
= l × b
if length=x m and breadth = y m, then base area = x y=4 sq.m
cost of construction of base = cost × base area
= 280 ×xy =1120sq.m
area of four sides of the tank = 2( lh+bh)
= 2( x×2 +y×2)
= 2(2x+2y)
= 2×2(x+y)
Area of four sides of tank = 4(x+y)sq.m
Cost of construction of sides of the tank = cost per sq.m×area of sides
=180×4(x+y)
=Rs. 720(x+y)
Therefore answer is Option (c) Rs. 720(x+y).
(3) Cost of construction of the tank = cost of base +cost of sides
= Rs.1120+ Rs.720(x+y)
C = Rs.1120+ Rs.720(x+4/x)
So the answer is option (a) C =1120+720(x+4/x)
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