A builder wants to build a sump to store water in an apartment. The volume of the
rectangular sump will be modelled by v(x) = x + x² - 4x – 4.
i) He planned in such a way that its base dimensions are (x + 1) and (x + 2). How much
he has to dig?
ii) If x = 4 meter, what is the volume of the sump?
iii) x = 4 and the builder wants to paint the entire inner portion on the sump, what is the
total area to be painted?
iv)If the cost of paint is Rs. 25/ per square metre, what is the cost of painting?
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Answers
A Builder wants to build a sump to store water in an apartment. The volume of the
rectangular sump will be modelled by v(x) = x + x² - 4x – 4.
i) He planned in such a way that its base dimensions are (x + 1) and (x + 2). How much
he has to dig?
ii) If x = 4 meter, what is the volume of the sump?
iii) x = 4 and the builder wants to paint the entire inner portion on the sump, what is the
total area to be painted?
iv)If the cost of paint is Rs. 25/ per square metre, what is the cost of painting?
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- 4x4
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
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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