Question

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four
walls at the rate of 10 per m'is 15000, find the height of the hall.
Hint: Area of the four walls =Lateral surface area.]
17​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Perimeter of floor = 250m

• Cost of painting the four walls at the rate of 10/m is 15000.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Height of the hall.

$\\ \\ \large\underline{ \underline{ \sf{ \red{formula:} }}}$

$\star \: \small \sf{total \: surface \: area \: of \:cuboid = 2(lh + bh + lb) } \\ \\ \small \sf \star \: curved \: surface \: area \: of \: cuboid = 2h(l + b) \\ \\ \small\star \sf \: perimeter \: of \: rectangle = 2(l + b)$

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Perimeter of floor = 250m

➜ 2 ( l + b ) = 250 ㅤㅤㅤㅤㅤ( 1 )

➥ Cost of painting walls = 15000 at 10/m

Area of 4walls ( C.S.A ) = 15000/10

➜ 2h( l + b ) = 1500ㅤㅤㅤㅤ(2)

From eqⁿ (1) , 2( l + b ) = 250

Putting in eqⁿ (2) ,

➣ h ( 250 ) = 1500

➣ h = 1500/250

∴ h = 6m

$\ \\ \therefore \: \sf \: height \: of \: the \: hall \: is \: 6m.$