Question

10. A rectangular bin, open at the top, is required to contain 128 cubic meters. If the bottom is to be square, at a cost
RM2 per square meter, while the sides cost RMO 50 per square meter, what dimensions will minimize the cost? [base-4
height=8]​

Answer 1

Step-by-step explanation:

A rectangular bin, open at the top, is required to contain 128 cubic meters. If the bottom is to be square, at a cost

RM2 per square meter, while the sides cost RMO 50 per square meter, what dimensions will minimize the cost? [base-4

height=8]

Answer 2

Answer:

Length =4m, breadth = 4m, height = 8m and the cost = Rs.92.

Step-by-step explanation:

Given:

base = 4 m, height =8m.

volume of rectangular bin(open at top) =128 cubic meter.

  that is,        l ×b ×h = 128 m³

                     4×b×8 = 128

                      b  =128/32 = 4

therefore breadth = 4m

since base is a square , area of square = 4×4 = 16m².

sides of rectangular bin are rectangle, then

  area of one side = l × b = 4×8 = 32m²

so, area of 4 sides of rectangular bin = 4×32 = 128m²

cos of painting the bottom per square meter= Rs.2

∴ cost of paining the bottom area = 16×2 = Rs.32

Also cost of painting the sides per square meter = Rs.50

∴ the cost of painting the four sides if the bin = 128×50 = Rs.6400

Hence total cost of painting the rectangular bin(top open) = Rs.32+Rs.6400 = Rs.6432'

Thus the dimensions  l = 4m ,b = 4m and h=8m will minimise the cost and the cost is Rs.6432.

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