Question

hei guys can u answer this question pls​

Answer 1

Question :

• The length and breadth of a room are in the ratio of 4:3 . The cost of decorating the walls of the room at the rate of Rs. 3.50 per m² is Rs. 2695.if the height of the room is 55 m. find the length of the room.

Answer :

• Let the Length of the room be 4x and Breadth of the room be 3x.
• Height of the room is 55 m.
• Rate of decorating the wall = Rs. 3.50 per m²
• Total cost of decorating wall = Rs. 2695

We need to find the Length of the room.

◖ According to the Question Now :

⇥ Total cost = area to be decorated × rate of decorating the wall

⇥ 2695 = 2( Length × Height + Breadth × Height) × 3.50

⇥ 2695 = 2 × Height (Length + Breadth) × 3.5

⇥ 2695 = 2 × 55 (4x + 3x) × 3.5

⇥ 2695 = 110 × 7x × 3.5

⇥ 2695 = 385 × 7x

⇥ 2695 ÷ 385 = 7x

⇥ 7 = 7x

⇥ x = 7 ÷ 7

⇥ x = 1

● DIMENSIONS :

• Length of the room = 4x = 4(1) = 4 m
• Breadth of the room = 3x = 3(1) = 3 m

⛬ The Length of the room is 4 m.

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Question :

• The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area and (iii) volume.

Answer :

• The diameter of the cylinder is 28 cm.
• Hence, the radius of the cylinder is 14 cm.
• Height of the cylinder is 21 cm.

◖ According to the Question Now :

⇸CSA of cylinder = 2πrh

⇸CSA of cylinder = 2 × 22/7 × 14 × 21

⇸CSA of cylinder = 2 × 22 × 2 × 21

⇸CSA of cylinder = 1,848 cm²

∴ The curved surface area of the right circular cylinder is 1,848 cm²

⇥ TSA of cylinder = 2πr(h + r)

⇥ TSA of cylinder = 2 × 22/7 × 14 (21 + 14)

⇥ TSA of cylinder = 2 × 22 × 2 (35)

⇥ TSA of cylinder = 88 × 35

⇥ TSA of cylinder = 3,080 cm²

∴ The total surface area of the right circular cylinder is 3,080 cm².

⇥ Volume of cylinder = πr²h

⇥ Volume of cylinder = 22/7 × (14)² × 21

⇥ Volume of cylinder = 22 × 196 × 3

⇥ Volume of cylinder = 12,936 cm³

∴ The volume of the right circular cylinder is 12,936 cm³.

Answer 2

Question :-

• The Length and Breadth of a room are in the ratio 4:3. The cost of Decorating the walls of the room at the rate of Rs, 3.50per m² is Rs, 2695. If the Height of the room is 55cm , find the length of the room.

Given :-

• Ratio of Length and Breadth is 4:3
• Height of the Room = 55m
• Rate of decorating the Walls = Rs, 3.50 per m³
• Total cost of Decorating the walls = Rs, 2695

To Find :-

• Length of the Room .

Solution :-

Let the Length be 4x

Let the Breadth be 3x

★ According to the Question ★

➳ Total Cost = Area to be decorated × rate of decoration

⇛ 2695 = 2 × Height ( Length + Breadth ) × Rate

⇛ 2695 = 2 ×55 ( 4x + 3x ) × 3.5

⇛ 2695 = 110 × 7x × 3.5

⇛ 2695 = 385 × 7x

⇛ 2695/385 = 7x

⇛ 7 = 7x

⇛ 1 = x

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Length = 4x = 4 × 1 = 4m

Breadth = 3x = 3 × 1 = 3m

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Verification :-

⇒2695 = 2 × Height ( Length + Breadth ) × Rate

⇒ 2695 = 2 × 55 ( 4 + 3 ) × 3.5

⇒ 2695 = 2 × 55 × 7 × 3.5

⇒2695 = 2695

Hence Verified

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$\therefore \sf Length \: = \: 4m$

$\therefore \sf Breadth \: = \: 3m$

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