Question

14. Nishant owns a house of dimensions 10 feet x 8 feet x 9 feet. His house has two entry doors on the opposite sides, of dimension 7 feet by 3 feet each and two windows on opposite walls of dimensions 3 ft x 2 f each. He wants wall papering to be done in his house. If the wallpaper that he selects is 2 ft wide and the cost is Rs. 25/ ft. Find the total cost paid by Nishant, if the labour charges Rs. 10/sq feet.​

Answer 1

Given :

• Dimesions of room is 10 feet x 8 feet x 9 feet .
• It has two entry doors of dimensions 7 feet × 3 feet .
• It has two windows on opposite walls of dimensions 3 feet × 2 feet .
• The wallpaper chosen by him costs Rs.25/ 2 feet²
• Labour charges are Rs.10 /feet² .

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To Find :

• Total Cost paid by Nishant = ?

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Solution :

~ Formula Used :

• Surface Area of Cuboid :

$\large{\blue{\dashrightarrow \: \: {\underbrace{\underline{\orange{\sf{ Lateral \: Surface \: Area{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}}}$

• Area of Rectangle :

$\large{\blue{\dashrightarrow \: \: {\underbrace{\underline{\orange{\sf{ Area{\small_{(Rectangle)}} = Length \times Breadth }}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Surface Area of Room :

${\longmapsto{\qquad{\sf{ Surface \: Area{\small_{(Room)}} = 2(lb + bh + hl) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area{\small_{(Room)}} = 2[(10 \times 8) + (8 \times 9) + (9 \times 10)] }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area{\small_{(Room)}} = 2 ( 80 + 72 + 90) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{Surface \: Area{\small_{(Room)}} = 2 \times 242 }}}} \\ \\ \ {\qquad{\textsf{ Surface Area of the Room = {\pink{\sf{ 484 \: feet² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Area of Door and Window :

• Area of Door :

${\longrightarrow{\qquad{\sf{ Area = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area = 7 \times 3 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Door = {\red{\sf{ 21 \: feet² }}}}}}$

• Area of Window :

${\longrightarrow{\qquad{\sf{ Area = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area = 3 \times 2 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Door = {\red{\sf{ 6 \: feet² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Total Area covered by Doors and Windows :

➳ As the No. of doors is 2 . Hence,

${:\implies{\qquad{\sf{ Area{\small_{(Two \: Doors)}} = Area{\small_{(One \: Door)}} \times 2 }}}} \\ \\ \ {:\implies{\qquad{\sf{ Area{\small_{(Two \: Doors)}} = 21 \times 2 }}}} \\ \\ \ {\qquad{\textsf{ Area of two Door = {\red{\sf{ 42 \: feet² }}}}}}$

➳ As the No. of windows on opposite walls is 2 so total no. of windows are 4 .Hence,

${:\implies{\qquad{\sf{ Area{\small_{(Four \: Windows)}} = Area{\small_{(One \: Window)}} \times 2 }}}} \\ \\ \ {:\implies{\qquad{\sf{ Area{\small_{(Four \: Windows)}} = 6 \times 4 }}}} \\ \\ \ {\qquad{\textsf{ Area of two Door = {\red{\sf{ 24 \: feet² }}}}}}$

➳ Now, Total Area Covered :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Covered)}} = Area{\small_{(Windows)}} + Area{\small_{(Doors)}} }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Covered)}} = 42 + 24 }}}} \\ \\ \ {\qquad{\textsf{ Total Area Covered = {\color{maroon}{\sf{ 66 \: feet² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Cost of Wallpaper :

${\longmapsto{\qquad{\sf{ Cost{\small_{(Wallpaper)}} = \dfrac{Area{\small_{(Room)}} - Area{\small_{( Doors \: and \: Windows)}}}{2} \times Rate }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Wallpaper)}} = \dfrac{484 - 66}{2} \times 25}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Wallpaper)}} = \cancel\dfrac{418 }{2} \times 25 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Wallpaper)}} = 209 \times 25 }}}} \\ \\ \ {\qquad{\textsf{ Cost of the Wallpaper = {\green{\sf{ ₹ \: 5225 }}}}}}$

~ Calculating the Cost of Labour :

${\longmapsto{\qquad{\sf{ Cost{\small_{(Labour)}} = Area \times Rate }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Labour)}} = 418 \times 10 }}}} \\ \\ \ {\qquad{\textsf{ Cost of Labour = {\orange{\sf{ ₹ \: 4180 }}}}}}$

~ Calculating the Total Cost :

${\longmapsto{\qquad{\sf{ Cost{\small_{(Total)}} = Cost{\small_{(Labour)}} + Cost{\small_{(Wallpaper)}} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Total)}} = Rs.5225 + Rs.4180 }}}} \\ \\ \ {\qquad{\textsf{ Total Cost paid by Nishant = {\purple{\sf{ ₹ \: 9405 }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Therefore :

❝ Nishant paid ₹ 9405 for wallpapering the room . ❞

$\\ {\pink{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}{\red{\underline{\rule{75pt}{9pt}}}}$

Answer 2

Suface Area of Cuboid = 2(lb + bh + hl)

Surface Area of Room :

⇒ 2(10*8 + 9*10 + 8*9)

⇒ 2(80 + 90 + 72)

⇒ 2(242)

⇒ 484 ft²

Area of Rectangle = L*B

Area of Door :

⇒ 7*3

⇒ 21 ft²

∴ Area of two Doors = 42 ft²

Area of Windows :

⇒ 3*2

⇒ 6 ft²

∴ Area of two Windows = 12 ft²

Total Cost Paid By Nishant :

⇒ 25 * (484 - 12 - 42) + 10 * (484 - 12 - 42)

⇒ 25 * (430) + 10 * (430)

⇒ 10,750 + 4300

⇒ ₹ 15,050

$\Huge{ \pink{ \underline{■■■}} \purple{ \underline{■■■}} \orange{ \underline{■■■}} \green{ \underline{■■■}} }$

∴ Total Cost paid by Nishant = ₹ 15,050