A builder wants to build a sump to store water in an apartment. He planned in such a
way that its base dimensions are (x + 1) and (x-2).
Questions:
1.1. Find how much he has to dig so that the volume of the rectangular prism will be
f(x) = x++ 2x - 4x - 7x-2.
1.2 If x=10 units, what is the volume of the sump?
1.3 If x = 10 and the builder wants to paint the outer portion on the sump, what is
the roct of naintine if the rost of naint is Rs 25/ ner snuare unit
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=10 units, what is the volume of the sump
=> V(10) = (10 + 2)(10 - 2)(10 + 1) = 12 x 8 x 11 = 1,056 cubic units
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
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