Question

length of an auditorium width height 24.5m 12m and 20m. find the area of the four walls and the roof also find the Find the cost of whitewashing on the ceiling and the four walls, while the cost of whitewashing is Rs 5 per square meter.​

Answer 1

Given

Length of an auditorium width height 24.5m 12m and 20m. The cost of whitewashing is Rs 5 per square meter.

To Find

find the area of the four walls and the roof also find the Find the cost of whitewashing on the ceiling and the four walls

Solution

• Length of auditorium (l) = 24.5 m
• Width of auditorium (b) = 12 m
• Height of auditorium (h) = 20m

★ Lateral surface area of walls = Area of four walls

→ 2(l + b)h

→ 2(24.5 + 12)20

→ 2*36.5*20

→ 1460 m²

★Area of ceiling

→ length × breadth

→ 24.5 × 12

→ 294 m²

★Now, the area of ceiling and four walls

→ 1460 + 294 = 1754 m²

★If the cost of whitewashing is Rs 5 per square metre then,

The cost of whitewashing on the ceiling and the four walls

= 5*1754

= Rs.8770

Hence, the cost of whitewashing on ceiling and the four walls is rs.8770

Answer 2

GIVEN :-

◙ Length of an auditorium(l) = 24.5 m

◙ Width of the auditorium(w) = 12 m

◙ Height of the auditorium(h) = 20 m

$\boxed{\underline{\rule{180}{2}}}$

TO FIND :-

♠ Area of the four walls and the roof.

♠ Cost of whitewashing on the ceiling and the four walls, while the cost of whitewashing is ₹ 5 per m².​

$\boxed{\underline{\rule{180}{2}}}$

SOLUTION :-

We know,

$\bigstar$ The LSA of the auditorium = Area of the 4 walls of the auditorium

$\boxed{\sf{LSA\ of\ a\ cuboid=2h(l+w)}}$

Substituting the values :-

$\sf{LSA=2\times20(24.5+12)}\\\\\sf{\longrightarrow LSA=40(36.5)}\\\\\underline{\boxed{\sf{\longrightarrow 1460\ m^2}}}$

$\rule{150}2$

Now,

Area of the roof = Length × Width

$\sf{\longrightarrow Area\ of\ the\ roof = 24.5 \times 12}\\\\\underline{\boxed{\sf{\longrightarrow Area\ of\ the\ roof = 294\ m^2}}}$

$\rule{150}2$

Total area of the 4 walls and the roof = 1460 + 294 = 1754 m²

Cost of whitewashing in ₹ 5 per m² = 5 × 1754

⇒Cost of whitewashing in ₹ 5 per m² = ₹ 8770

Therefore, the cost of whitewashing the four walls along-with the roof of the auditorium is ₹ 8770.