Question

0. A hall has 4 windows, each 4 m wide and 2 m high,
2 doors, each 2.5 m tall and 2 m wide, and 3 wall
closets, each 2.5 m tall and 1 m wide. If the hall is
20 m long, 18 m wide, and 6 m high, find the cost of
painting its walls at * 38 per
m.
th​

Answer 1

Answer:

₹ 15447.0

Step-by-step explanation:

Area of the wall that should be painted =

Lateral surface area of the cuboid - area of the 4 windows - area of the 2 doors - area of the 3 wall closets .....

= { 2 × 6 (18+20) - 4 × ( 4×2 ) - 2× ( 2.5 ×2 ) - 3( 2.5×1 ) } m^2

= { 12 × 38 - 32 - 10 - 7.5 } m^2

= { 456 - 49.5 } m^2

= { 406.5 } m^2

Cost of painting its walls at ₹ 38 per m^2 =

₹ (406.5 × 38)

₹ 15447.0

Answer 2

$\large\underline{\sf{Solution-}}$

Dimensions of Room :-

• Length of room, l = 20 m

• Breadth of room, b = 18 m

• Height of room, h = 6 m

We know,

Area of 4 walls of a room is given by

$\rm :\longmapsto\:Area_{(4 \: walls)} = 2(l \: + \: b) \times h$

$\rm :\longmapsto\:Area_{(4 \: walls)} = 2(20\: + \: 18) \times 6$

$\rm :\longmapsto\:Area_{(4 \: walls)} = 12 \times 38$

$\bf :\longmapsto\:Area_{(4 \: walls)} = 456 \: {m}^{2}$

Dimensions of window :-

• Breadth of window = 4 m

• Height of window = 2 m

• Number of windows = 4

So,

$\rm :\longmapsto\:Area_{(4 windows)} = 4 \times 4 \times 2$

$\bf :\longmapsto\:Area_{(4 \: windows)} = 32 \: {m}^{2}$

Dimensions of door :-

• Breadth of door = 2m

• Height of door = 2.5 m

• Number of doors = 2

So,

$\rm :\longmapsto\:Area_{(2 \: doors)} = 2 \times 2 \times 2.5$

$\bf :\longmapsto\:Area_{(2 \: doors)} = 10 \: {m}^{2}$

Dimensions of closets :-

• Breadth = 1 m

• Height = 2.5 m

• Number of closets = 3

So,

$\rm :\longmapsto\:Area_{(3 \: closets)} = 3 \times 1 \times 2.5$

$\bf :\longmapsto\:Area_{(3 \: closets)} = 7.5 \: {m}^{2}$

Thus,

$\bf :\longmapsto\:Area_{(of \: walls \: to \: be \: white - washed)}$

$\rm \: \: = \: Area_{(4 walls)} - Area_{(4 \: windows)} - Area_{(2 \: doors)} - Area_{(3 \: closets)}$

$\rm \: \: = \: 456 - 32 - 10 - 7.5$

$\rm \: \: = \: 406.5 \: {m}^{2}$

Now,

$\rm :\longmapsto\:Cost \: of \: painting \: 1 \: {m}^{2} \: is \: Rs \: 38$

$\rm :\longmapsto\:Cost \: of \: painting \: 4065 \: {m}^{2} \: = \: \: 38 \times 406.5$

$\bf :\longmapsto\:Cost \: of \: painting \: 4065 \: {m}^{2} \: = \: Rs \: 15447$

Additional Information

☆ Cube: 

• A cube is a three-dimensional shape has six faces, eight vertices and twelve edges.

☆ Cuboid: 

• A cuboid having six faces, eight vertices and twelve edges.

☆ Formula's of Cube :-

• Total Surface Area = 6(side)²

• Curved Surface Area = 4(side)²

• Volume of Cube = (side)³

• Diagonal of a cube = √3(side)

• Perimeter of cube = 12 x side

☆ Formula's of Cuboid

• Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

• Curved Surface area = 2 height(length + breadth)

• Volume of the cuboid = (length × breadth × height)

• Diagonal of the cuboid =√(l² + b² + h²)

• Perimeter of cuboid = 4 (length + breadth + height)