Question

The dimensions of a hall is 10 mx9m x 8 m. Find the cost of white washing the
walls and ceiling at the rate of 78.50 per m^2​

Answer 1

Solution :

The dimensions of a cuboidal hall are 10 m × 9 m × 8 m

To finD

Cost of White Washing the Walls and Ceiling

There are two approaches to solve the given question

• We find the Total Surface Area of the hall and subtract the area of floor from the latter,which would give us the area required to be painted

• We can find the Lateral Surface Area of tne hall and add the area of the ceiling,which would give us the area to be painted

Now,

• Length,l = 10 m
• Breadth,b = 9 m
• Height,h = 8 m

Total Area to be PainteD

$\implies \sf LSA + Area \ of \ Ceiling \\ \\ \implies \sf 2h(l +b) + (l \times b) \\ \\ \implies \sf 2(8)(10 + 9) + (10 \times 9) \\ \\ \implies \sf 394 {m}^{2}$

The total area to be painted is 394 m²

Now,

The cost of painting one m² is 78.50 rupees

The cost of painting 394 m² would be :

$\implies \: \sf \: 394 \times 78.50 \\ \\ \implies \: \sf \: Rs \ 30929 \:$

Answer 2

$\Huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\large \tt Given \begin{cases} \sf{Length \: (L) \: = \: 10 \: m} \\ \sf{Breadth \: (B) \: = \: 9 \: m} \\ \sf{Height \: (H) \: = \: 8 \: m} \\ \sf{Cost \: = \: 78.5 \: per \: m^2} \end{cases}$

As we have to find cost of white washing of four walls and a roof also. So, We have to find area of walls and roof.

So, Total Area = Area of Four Walls + Area of Roof

$\rule{100}{1}$

Area of Four Walls :

Use Curved Surface Area,

$\large \bigstar{\boxed{\sf{C.S.A \: = \: 2(L \: + \:B)H}}} \\ \\ \implies {\sf{C.S.A \: = \: 2(10 \: + \: 9) \: \times \: 8}} \\ \\ \implies {\sf{C.S.A \: = \: 2(19) \: \times \: 8}} \\ \\ \implies {\sf{C.S.A \: = \: 38 \: \times \: 8}} \\ \\ \implies {\sf{C.S.A \: = \: 304}} \\ \\ \large {\boxed{\sf{C.S.A \: = \: 304 \: m^2}}}$

$\rule{150}{0.5}$

Area of Roof :

Use formula for area of triangle

$\large \bigstar{\boxed{\sf{Area \: = \: L \: \times \: B}}} \\ \\ \implies {\sf{Area \: = \: 10 \: \times \: 9}} \\ \\ \implies {\sf{Area \: = \: 90}} \\ \\ \large {\boxed{\sf{Area \: of \: Roof \: = \: 90 \: m^2}}}$

$\rule{100}{1}$

Area for White Washing :

$\large \bigstar {\boxed{\sf{Area \: = \: C.S.A \: + \: Roof \: Area}}} \\ \\ \implies {\sf{Area \: = \: 304 \: + \: 90}} \\ \\ \implies {\sf{Area \: = \: 394}} \\ \\ \large {\boxed{\sf{Area \: = \: 394 \: m^2}}}$

$\rule{200}{2}$

Cost of White Washing :

$\large \bigstar {\boxed{\sf{Cost \: = \: Area \: \times \: Cost \: per \: m^2}}} \\ \\ \implies {\sf{Cost \: = \: 394 \: \times \: 78.5}} \\ \\ \implies {\sf{Cost \: = \: 30929}} \\ \\ \large {\boxed{\sf{Cost \: = \:Rs. \: 30,929}}}$