Question

A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be
modelled by

(i) He planned in such a way that its base dimensions are . How much he has to dig?
a) (x+1) b)(x+2) c)(x+3) d) (x+4)

(ii) If is 4 meter, what is the volume of sump?
a) 30 b) 15 c) 20 d) 60 [1]

(iii) If = 4 and the builder wants to pant the entire inner portion on the sump, what is the total is to be
painted?
a) 102 b) 52 c) 96 d) none of these [1]

(iv) If the cost of paint is Rs.25 per square meter, what is the cost of painting? [1]
a) Rs.1300 b) Rs.2600 c) Rs.3900 d) Rs.5200

(v) What is the storage capacity of this tank? [1]
a) 3000 L b) 6000 L c) 30000L d) 60000 L​

Answer 1

SOLUTION

COMPLETE QUESTION

A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

i) He planned in such a way that its base dimensions are (x + 1) and (x + 2). How much he has to dig

a) (x+1)

(b) (x-2)

(c) (x-3)

(d) (x+2)

EVALUATION

Here it is given that A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

We now simplify it as below

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

$\implies \: \sf{v(x) = {x}^{2} (x + 1) - 4(x + 1) }$

$\implies \: \sf{v(x) = ( {x}^{2} - 4) (x + 1) }$

$\implies \: \sf{v(x) = ( {x}^{2} - {2}^{2} ) (x + 1) }$

$\implies \: \sf{v(x) = ( x + 2 ) (x - 2)(x + 1) }$

Now the builder has planned in such a way that its base dimensions are (x + 1) & (x + 2)

Hence the builder has to dig

$\displaystyle \sf{ = \frac{v(x)}{(x + 1)(x + 2)} }$

$\displaystyle \sf{ = \frac{(x + 2)(x - 2)(x + 1)}{(x + 1)(x + 2)} }$

$\displaystyle \sf{ = x - 2}$

Hence the correct option is (b) (x-2)

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Answer 2

Answer:

ii) d) 60

Step-by-step explanation:

(4)3 + (4)2 - 4(4)-4

60