Question

1. The l,b,h of a room are 5m,4m,3m.Find the cost of painting the walls and cellieng at the rate of RS.10.50per m.square
2.The diameter of a roller is 84cm and its lenght = 120cm.It takes 200 revolution.Find the area it covers.

Answer 1

Answer:

Step-by-step explanation:

Answer:-

Given that

• Length is 5 m,

• Breadth is 4 m

• Height is 6 m.

We need the cost of painting walls and ceiling, so we will take the total Surface area of the room.

TSA of Cuboid = 2(lb+bh+hl) - lb

= 2(5×4+4×3+3×5) -20

= 2(20+12+15) -20

= 74

= 74 m² is the total area.

Now,

1m² = 10.5

74 = 10.5 × 74

= Rs. 777 is the required answer.

2. Diameter = 2 times Radius.

So, Radius is 84/2 = 42 cm

Now, Area we need to find.

Area it covers = CSA of the roller × the number of times it rolled .

= 2 × $\pi$ × 42 × 120 ( Given as its length)

= 2 × $\pi$ × 42 × 120

= 31680 cm.

Now, area it covers = 31680 × 200

= 6336000 cm² is the required area.

Answer 2

Answer :-

$\: \: \underline{\boxed{\sf{\purple{\mapsto \: \: Let's \: analyse \: the \: question \: first}}}}$

• For 1.) We are given the dimensions of the wall of room and we need to fid out the cost of painting. We know that the floor of any room isn't painted, so anyhow we have to calculate the TSA of the room and then subtract the area of the rectangular floor.

• For 2.) We are given the dimensions of roller.In order to find the area that it covered, then we have to multiply its CSA with the number of revolutions it took.

_____________________________________

★ Formula Used :-

$\: \: \boxed{\rm{\red{\Longrightarrow \: \: \: TSA \: of \: Cuboid \: = \: 2 \: \times \: (lb + bh + lh)}}}$

$\: \: \boxed{\rm{\red{\Longrightarrow \: \: \: Area \: of \: Rectangular \: Plane \: = \: Length (L) \: \times \: Breadth(B)}}}$

$\: \: \boxed{\rm{\red{\Longrightarrow \: \: \: CSA \: of \: Cylindrical \: Solid \: = \: 2\pi rh}}}$

_____________________________________

★ Solution :-

1.) The l,b,h of a room are 5m,4m,3m.Find the cost of painting the walls and ceiling at the rate of Rs. 10.50 per m².

Answer .)

Given,

» Length of the room = L = 5 m

» Breadth of the room = B = 4 m

» Height of the room = H = 3 m

» Cost of painting = ₹ 10.5 per m²

Now using the formula we get,

➔ Area to be painted = 2 × [(lb) + (bh) + (lh)] - (l×b)

➔ Area to be painted = 2 × [(5×4) + (4×3) + (3×5)] - (5 × 4)

➔ Area to be painted = 2 × [20 + 12 + 15] - 20

➔ Area to be painted = 2 × 47 - 20

➔ Area to be painted = 94 - 20

➔ Area to be painted = 74 cm²

Now total cost of painting, is given as :

⌬ Total cost of painting = Rate (per m²) × Area to be painted

⌬ Total cost of painting = 10.50 × 74 cm²

⌬ Total cost of painting = ₹ 777

$\: \: \underline{\boxed{\rm{\green{\Longrightarrow \: \: \: Hence, \: total \: cost \: of \: painting \: the \: walls \: and \: ceilings \: is \: \underline{₹ \: 777}}}}}$

_____________________________________

2.) The diameter of a roller is 84 cm and its length is 120 cm.It takes 200 revolution.Find the area it covers.

Answer.)

Given,

» Diameter of the roller = d = 84 cm

» Radius of the roller = r = ½(d) = ½(84) = 42 cm

» Number of revolutions taken = 200

» Length of roller = h = 120 cm

By using the formula, we get,

⌬ Area covered by roller = CSA of Cylinder × number of revolutions

⌬ Area covered by roller = 2πrh × 200

$\: \: \: \pink{\bf{\Longrightarrow \: \: \: Area \: covered \: by \: roller \: = \: 2 \: \times \: \dfrac{22}{7} \: \times \: 42 \: \times \: 120 \: \times \: 200}}$

⌬ Area covered by roller = 6336000 cm²

$\: \: \underline{\boxed{\sf{\orange{\Longrightarrow \: \: Hence, \: the \: area \: covered \: by \: roller \: is \: \underline{63,36,000 \: cm^{2}}}}}}$

_______________________________

$\: \: \underline{\boxed{\sf{\blue{\mapsto \: \: \: Please \: refer \: to \: Supplementary \: Counsel}}}}$

• Volume of Cube = (Side)³

• Volume of Cuboid = Length × Breadth × Height

• Volume of Cylinder = πr²h

where r is the radius and h is the height/length.

• Volume of Cone = ⅓(πr²h)

• TSA of Cube = 6 × (side)²

• CSA of Cube = 4 × (side)²

• TSA of Cylinder = 2πrh + 2πr²