A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is melted and cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. The length of the pipe will bea)130 mb)102 mc)112 md)120 mCorrect answer is option 'C'. Can you explain this answer?

Question

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is melted and cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. The length of the pipe will be&#8203;a)130 mb)102 mc)112 md)120 mCorrect answer is option 'C'. Can you explain this answer?

Answer

Bhai dekh, baat aisi hai ki jab rectangular block ko pipe me mould kara gya toh dono ka volume toh same hi rhega na... thik hai na thik hai.. Ha toh ab dekh...bole toh,..⇒ l × b × h = π(R² - r²)h   ⇒ 4.4 × 2.6 × 1 = π[ (0.35)² - (0.3)² ]h  ⇒ h = (4.4 × 2.6)/(3.142 × 0.0325) = 112.03 m  Dikhe samjh hi gya hoga... na smjha ho toh fir se padh le ... dhanyawad..

Answer

Here is your answer Given = a solid square of dimension (4.4×2.6×1)m³To prove = length of pipe proof = A/q Bigger radius of cylinder = (30+5)cm= 35/100 msmaller radius of cylinder = 30cm= 30/100 min a hollow cylener = (πR² - πr²) = π(R² - r²)= 22/7(35² - 30²)= 22/7(35 + 30)(35 - 30)= 22/7×65/100×5/100now length of pipe = πR'²length length of pipe = πR'²h = volume of square πR'²h = 4.4×2.6×1= 22/7×65/100×5/100×h = 4.4×2.6×1h= 11.44/0.1021428571h = 112 mtherefore the length of pipe is 112 mthanks

Answer

Given:
Dimensions of the solid iron rectangular block:
Length (l) = 4.4 m
Width (w) = 2.6 m
Height (h) = 1 m

Dimensions of the hollow cylindrical pipe:
Internal radius (r) = 30 cm = 0.3 m
Thickness (t) = 5 cm = 0.05 m

We need to find the length of the pipe.

Step 1: Calculate the volume of the solid iron rectangular block
The volume of the rectangular block is given by the formula:
Volume = length × width × height

Substituting the given values, we get:
Volume = 4.4 m × 2.6 m × 1 m
Volume = 11.44 m³

Step 2: Calculate the volume of the hollow cylindrical pipe
The volume of the hollow cylindrical pipe is given by the formula:
Volume = π × (Outer radius² - Inner radius²) × height

Given that the thickness of the pipe is 0.05 m, the outer radius can be calculated as follows:
Outer radius = Internal radius + Thickness
Outer radius = 0.3 m + 0.05 m
Outer radius = 0.35 m

Substituting the values, we get:
Volume = π × (0.35 m)² - (0.3 m)² × height
Volume = π × (0.1225 m² - 0.09 m²) × height
Volume = π × 0.0325 m² × height

Step 3: Equate the volumes of the rectangular block and the cylindrical pipe
Since the solid iron rectangular block is melted and cast into the cylindrical pipe, the volume of the rectangular block should be equal to the volume of the pipe.

Therefore, we have:
11.44 m³ = π × 0.0325 m² × height

Step 4: Solve for the height of the pipe
Dividing both sides of the equation by π × 0.0325 m², we get:
height = 11.44 m³ / (π × 0.0325 m²)
height = 112 m

Therefore, the length of the pipe is 112 m, which corresponds to option C.

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