Question

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) = x3 + x2 - 4x - 4.
He planned in such a way that its length and breadth are (x + 1) and (x - 2) respectively.
How much he has to dig?
(a) (x + 1]
(b) (x - 2)
(c) (x-3)
(d) (x + 2)
(ii) If x = 4 meter, what is the storage capacity (in litres) of this sump?
(iii) A ladder is kept a point halfway from the base as shown in the figure. It just touches
the top of the sump. Find the length of the ladder, assuming x-42 (correct to 1 dp)​

Answer 1

Answer:

• 1) b, 2) d, 3) d

Step-by-step explanation:

The volume is the product of three dimensions

• V = lwh

Given:

w = x + 1, l = x + 2 and V(x) = x³ + x² - 4x - 4

1) Let's find the height:

• x³ + x² - 4x - 4 =
• x²(x + 1) - 4(x + 1) =
• (x² -4)(x + 1) =
• (x + 2)(x - 2)(x + 1)
• We got
• h = x - 2

2) x = 4 m

Volume is:

• V = 4³ + 4² - 4*4 - 4 = 60 m³

3) x = 4 m

Dimensions are:

• w = x + 1 = 5 m, l = x + 2 = 6 m, h = x - 2 = 2 m

Full surface area is:

• 2(lw + lh + wh) =
• 2(5*6 + 6*2 + 5*2) = 104 m²