Question

A cistern of capacity 8000litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5cm thick. The thickness of the bottom is

Answer 1

$\sf{\underline{Given:}}$

Length = $\sf{3.3\:m}$

Width = $\sf{2.6\:m}$

Height = $\sf{1.1\:m}$

$\sf{\underline{And:}}$

Volume of cistern = $\sf{8000\:L}$

Thickness of walls = $\sf{5\:cm}$

$\sf{\underline{To\:find:}}$

The thickness of the bottom of the tank.

$\sf{\underline{We\:know\:that:}}$

$\sf{1\:L}$ = $\sf{1000}$ cubic centimetres.

$\sf{\underline{Hence:}}$

$\sf{\underline{The\:length\:of\:cistern:}}$

$\implies$ $\sf{ 3.3 \times 100}$

$\implies$ $\sf{ 330 \: cm}$

$\sf{\underline{The\:width\:of\:cistern:}}$

$\implies$ $\sf{2.6 \times 100}$

$\implies$ $\sf{ 260 \: cm}$

$\sf{\underline{The\:height\:of\:cistern:}}$

$\implies$ $\sf{ 1.1 \times 100}$

$\implies$ $\sf{ 110 \: cm}$

$\sf{\underline{Now:}}$

The walls of the cistern are 5 cm thick.

$\sf{\underline{Hence:}}$

The inner length of the cistern is:

$\boxed{\sf{330 - 10 = 320 \: cm}}$

The inner width of the cistern:

$\boxed{\sf{260 - 10 = 250 \: cm}}$

$\sf{\underline{Now:}}$

$\sf{\underline{The\:total\: volume\:of\:the\:cistern\:is:}}$

$\implies$ $\sf{8000\:L}$ = $\sf{8000000}$ cubic centimetres.

$\implies$ $\sf{ 8000000 = 320 \times 250 \times x}$

$\sf{\underline{Let\:x\:be\:the\:internal\:height\:of\:the\:tank.}}$

$\implies$ $\sf{8000000 = 80000 \times x}$

$\implies$ $\sf{x = \frac{8000000}{80000} }$

$\implies$ $\sf{x = 100}$

$\sf{\underline{Hence:}}$

$\boxed{\sf{x = 100 \: cm}}$

$\sf{\underline{Thus:}}$

The thickness of the bottom is:

$\boxed{\sf{110 - 100 = 10 \: cm}}$

$\sf{\underline{Therefore:}}$

The thickness of the bottom is 10 centimetres.