Question

An open rectangular cistern is made of iron 2·5 cm thick. When measured from outside, it is 1 m 25 cm long, 1 m 5 cm broad and 90 cm deep. Find:
(i) the capacity of the cistern in litres;
(ii) the volume of iron used;
(iii) the total surface area of the cistern. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

External dimensions of the cistern are :

Length = 125 cm, Breadth = 105 cm and Depth = 90 cm.

Internal dimensions of the cistern are:

Length = 120 cm, Breadth = 100 cm and Depth = 87.5 cm.

(i) Capacity = Internal volume $=l\times b\times h=(120\times 100\times 87.5)c{m}^3$

$=\frac{(120\times 100\times 87.5)}{1000}litres=1050litres$. (1 litre= 1000$c{m}^3$)

(ii) Volume of iron = (External volume) - (Internal volume)

$=\left[\right(125\times 105\times 90)-(120\times 100\times 87.5\left)\right]c{m}^3$

$=(1181250-1050000)c{m}^3=131250c{m}^3$.

(iii) External area = (Area of 4 faces) + (Area of the base)

$=\left[2\right(125+105)\times 90]+(125\times 105)c{m}^2$

$=(41400+13125)c{m}^2=54525c{m}^2$.

Internal area $=\left[2\right(120+100)\times 87.5]+(120\times 100)c{m}^2$

$=(38500+12000)c{m}^2$

$=50500c{m}^2$.

Area at the top = Area between outer and inner rectangles

$=\left[\right(125\times 105)-(120\times 100\left)\right]c{m}^2$

$=(13125-12000)c{m}^2$

$=1125c{m}^2$.

Total surface area
$=(54525+50500+1125)c{m}^2=106150c{m}^2$.