Question

1. 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

Answer:

1. x-2

2. Ans :. 60 m cube

3. 104 m square

4. 2600 rs ..

all these ans are correct please like ..

Answer 2

The answers are x-2, 60, 104, 2600.

Given:

The volume of the rectangular sump is $v(x)=x^3 +x^2 -4x-4$.

Base dimensions are $x+1$ and $x+2$.

To Find:

Depth of the sump

The volume of the sump if x = 4.

Total inner are of the sump

Cost to paint the sump

Solution:

i)The volume of the rectangular sump is the multiplication of its height and base dimensions.

$V= a*b*h$

We have been given a and b and have to find h.

Therefore

$h = \frac{x^3 + x^2-4x-4}{(x+2)(x+1)} \\\\h=\frac{(x-2)(x+2)(x+1)}{(x+2)(x+1)} \\\\h=x-2$

Hence the builder has to dig $x-2$.

ii) If x = 4 m,

$v(4)=4^3 +4^2 -4*4-4\\\\v=60 m^3$

Hence the volume of the sump is 60.

iii) The entire inner portion is the entire surface area of the sump which is

$A=2((x+2)(x+1)+(x+2)(x-2)+(x+1)(x-2))$

For x = 4 m,

$A=2((4+2)(4+1)+(4+2)(4-2)+(4+1)(4-2))\\\\A=2(30+12+10)\\\\A=104 m^2$

Hence the total area to be painted is 104.

iv) Total cost to paint = Cost * Area

$Total cost = 25*104 =Rs.2600$

Hence the total cost is Rs. 2600.

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