pls ans above case study question from maths class 10...
Answers
Given :
volume of the rectangular sump V(x) = x³ + x²- 4x-4
base dimensions are (x + 1) and (x-2).
To Find : how much he has to dig
if x = 10 then Volume
if x = 4 then Volume
Solution:
V(x) = x³ + x²- 4x-4
base dimensions are (x + 1) and (x+2).
base area = (x + 1)(x + 2)
Depth = h
=> (x + 1)(x + 2)h = x³ + x²- 4x-4
=> (x + 1)(x + 2)h = x²(x + 1) -4(x + 1)
=> (x + 1)(x + 2)h = (x² - 4)(x + 1)
=> (x + 2)h = (x² - 4)
=> (x + 2)h = (x + 2)(x - 2)
=> h = x - 2
x-2 to be Digged
V(x) = (x + 2)(x - 2)(x + 1)
x=4 units, what is the volume of the sump
=> V(4) = (4 + 2)(4 - 2)(4 + 1) = 6 x 2 x 5= 60 cubic units
5 6 2
Surface area = (x + 1)(x+2) + (x - 2) 2(x + 1 + x + 2)
= (5)(6) + 2(2)(11)
= 30 + 44
= 74 m²
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