Question

A room has dimensions 34m × 24m × 8 m find the cost of white washing the four walls and celling at the rate of rs 10 per mcube

Answer 1

Given -

Length - 34 m

Breadth - 24 m

Height - 8 m

To find -

Cost of white washing the fours walls and the celling.

Solution -

Using the formula of lateral surface area of cuboid where -

L = Length

B = Breadth

H = Height

Lateral surface area of cuboid = 2(l+b)h

LSA of cuboid = 2(34 + 24)× 8 m

LSA of cuboid = 2(58)× 8 m

LSA of cuboid = 116 × 8 m

LSA of cuboid = 928 m³

Area of ceiling = L × B [As base of a cuboid is rectangle]

Area of ceiling = 34 × 24 m

⠀⠀⠀⠀⠀⠀ ⠀⠀ = 816 m²

Area of room to be whitewashed with ceiling too = Area of four walls + Area of ceiling

= 928 + 816 m²

= 1744 m²

Cost of whitewashing = 928 × 10 = ₹ 9280 m³

$\therefore$ The area of room including ceiling is 1744m² and cost of whitewashing the four walls + ceiling is ₹9280 per m³

______________________________________

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

A room has dimensions 34m × 24m × 8 m find the cost of white washing the four walls and celling at the rate of rs 10 per m cube.

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large{\boxed{\sf{\pink{✧ \: Given \: that}}}}$

• Length of the room = 34 m
• Breadth of room = 24 m
• Height of the room = 8 m
• Celling is at the cost of Rupees 10 per m³

$\large{\boxed{\sf{\pink{✧ \: To \: find}}}}$

• The cost of white washing the four walls.

$\large{\boxed{\sf{\pink{✧ \: Solution}}}}$

• The cost of white washing the four walls = Rupees 9280 m³

$\large{\boxed{\sf{\pink{We \: also \: write \: the \: following \: as}}}}$

$\mapsto$ $\large\blue{\texttt{Height as H}}$

$\mapsto$ $\large\green{\texttt{Length as L}}$

$\mapsto$ $\large\red{\texttt{Breadth as B}}$

$\mapsto$ $\large\red{\texttt{Lateral surface area as LSA}}$

$\large{\boxed{\sf{\pink{✧ \: Full \: solution}}}}$

$\large\gray{\texttt{Formula of LSA}}$

$\large\orange{\texttt{2[l+b]h}}$

$\large\purple{\texttt{Putting the values}}$

$\mapsto$ LSA = 2 × (34+24) × 8

$\mapsto$ LSA = 2 × 58 × 8

$\mapsto$ LSA = 116 × 8

$\mapsto$ LSA = 928 m³

$\large\gray{\texttt{Area of celling}}$

$\large\orange{\texttt{L×B}}$

{ As base of a rectangle's cuboid }

$\mapsto$ Area of celling = 34 × 24 m

$\mapsto$ Area of celling = 816 m²

$\large\gray{\texttt{Area of room to be whitewashed}}$

$\large\orange{\texttt{A of 4 wall + A of celling}}$

$\mapsto$ 928 + 816 m²

$\mapsto$ 1744 m²

$\large\purple{\texttt{Cost of whitewashing}}$

$\mapsto$ 928 × 10

$\mapsto$ Rupees 9280 m²

Hence, the area of of 4 wall is 1744 m² and the cost of whitewashing is Rupees 9280 m³.

$\large{\boxed{\boxed{\underline{\sf{Answer \: is \: 9280m{^3}}}}}}$

@Itzbeautyqueen23

Hope it's helpful

Thank you :)