Question

A room is 7 m long, 4 m broad and 3.5 m high. It has two doors each 1.5 m by 2 m and two windows each 75 cm by 75 cm calculate.

(a) Area of Walls and roof.

(b) The cost of white washing the wall and roof at Rs. 8 per m^2.​

Answer 1

A room is 7 m long, 4 m broad and 3.5 m high. It has two doors each 1.5 m by 2 m and two windows each 75 cm by 75 cm calculate.

(a) Area of Walls and roof.

(b) The cost of white washing the wall and roof at Rs. 8 per m^2.

Answer 2

Part (a) ↴

$\sf \: (a) \: Area \: of \: roof \: = \: Length \: \times \: Breadth$

$\sf \: = \: 7m \: \times \: 4m \: = \: 28m^{2}$

$\sf \: Area \: of \: 4 \: walls \: \: (Lateral \: Surface \: Area) \: = \: 2(L + B)h \: sq. \: unit$

$\sf \: = \: 2(7 + 4) \times 3.5 \: m^{2}$

$\sf \: = \: 2 \times 11\times 3.5 \: m^{2}$

$\sf \: = \: 77 \: m ^{2}$

Part (b) ↴

$\sf \: Area \: of \: two \: doors \: = \: 2 \: \times \: \: (1.5m \times 2m) \: = \: 2 \: \times \: 3.0 m ^{2}$

$\sf \: = 6.0 \: m\: ^{2}$

$\sf \: Area \: of \: two \: windows \: = \: 2 \: \times \: (75 cm \: \times \: 75 cm)$

$\sf \: = 2 \: \times \: (0.75 \times 0.75)$

$\sf \: = 2 \: \times \: (0.75 \times 0.75) \: = \: 1.125 \: m^{2}$

$\sf \: Area \: of \: Wall \: and \: the \: roof \: to \: be \: white \: washed \: =$

$\sf \: [{(Area \: of \: 4 \: walls) \: + \: (Area \: of \: roof)}] \: - [{(Area \: of \: door) + (Area \: of \: windows)}]$

$\sf \: = (77 \: m^{2} \: + \: 28 \: m ^{2} ) \: - \: (6.0 \: m ^{2} + 1.125 \: m \: ^{2} )$

$\sf \: = \: 105 \: m ^{2} \: - \: 7.125 \: m ^{2}$

$\sf \: = \: 97.875 \: m \: ^{2}$

$\sf \: Cost \: of \: White \: washing \: = \: Rs. (97.875 \: \times \: 8)$

$\sf \: \: Rs. \: 97.875 \: \times \: 8 \: = \: Rs. \: 783$