Question

Underground water sump is popular in India. It is usually used for large water sump
storage and can be built cheaply using cement-like materials. Underground water sump
are typically chosen by people who want to save space. The water in the underground
sump is not affected by extreme weather conditions. The underground sump maintain
cool temperatures in both winter and summer.
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?​

Answer 1

Given : The volume of the rectangular sump will be modelled by v(x) = x³ + x² - 4x – 4.

 base dimensions are (x + 1) and (x + 2).

To Find : How much he has to dig?

Solution:

v(x) = x³ + x² - 4x – 4.

= v(x) = x²(x + 1) - 4(x + 1)

=>  v(x) = (x + 1)(x² - 4)

=>  v(x) = (x + 1)(x + 2)(x - 2)

base dimensions are (x + 1) and (x + 2)

Hence (x - 2)  has to dig

x = 4 meter

Volume = (4 + 1)(4 + 2)(4 - 2)  =  60 m³

Base dimensions  5 , 6  Depth = 2

Area = 5 * 6  + 2(5 + 6) * 2

= 30 + 44

= 74 m²

total area to be painted = 74 m²

cost of paint is Rs. 25/ per square metre

Total Cost  = 25 x74

= 1850  Rs

Learn More:

A builder wants to build a sump to store water in an apartment. He ..

https://brainly.in/question/21608728

A cylinder is such that the sum of its height and circumference of its ...

brainly.in/question/11482028

pravali house has a water tank in the shape of a cylinder on the roof ...

brainly.in/question/7392846