Question

A solid iron rectangular block of dimensions (2.2m x1.2mx1m) is cast into a
hollow cylindrical pipe of internal radius 35 cm and thickness 5 cm. Find the
height (length) of the pipe.
​

Answer 1

Answer:

$\bigstar{\bold{Height\:of\:the\:pipe=22.4\:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\rm{Given:}}}}$

• Dimensions of the rectangular block = 2.2 m × 1.2 m × 1 m
• Internal radius of the pipe = 35 cm = 0.35 m
• Thickness of the pipe = 5 cm = 0.05 m

$\Large{\underline{\underline{\rm{To\:Find:}}}}$

• Height of the pipe

$\Large{\underline{\underline{\rm{Solution:}}}}$

➤ First we have to find the volume of the rectangular block in shape of a cuboid.

➤ The volume of a cuboid is given by,

   Volume of a cuboid =  length × breadth × height

➤ Substitute the data,

    Volume of the cuboid = 2.2 × 1.2 × 1

    Volume of the cuboid = 2.64 m³

➤ Hence volume of the cuboid is 2.64 m³

➤ Now we have to find the volume of the hollow cylindrical pipe.

➤ External radius of the pipe = Internal radius  + Thickness

    External radius = 0.35 + 0.05 = 0.4 m

➤ Now the volume of a hollow cylinder is given by,

    Volume of a hollow cylinder = π h (R² - r²)

    where R is the external radius and r is the internal radius

➤ Substitute the data,

    Volume of the hollow cylinder = 22/7 × h × (0.16 - 0.1225)

    Volume of the hollow cylinder = 22/7 × h × 0.0375

    Volume of the hollow cylinder = 0.118 h

➤ Here it is given that the cuboid is converted into the cylinder

➤ Hence,

    Volume of the cuboid = Volume of the hollow cylinder

     2.64 = 0.118 h

     h = 2.64/0.118

     h = 22.4 m

➤ Hence height or length of the pipe is 22.4 m

    $\boxed{\bold{Height\:of\:the\:pipe=22.4\:m}}$

$\Large{\underline{\underline{\rm{Notes}}}}$

➤ The volume of a cuboid is given by,

    Volume of a cuboid = l × b × h

    where l = length

    b = breadth

    h = height

➤ Volume of a hollow cylinder is given by,

    Volume of a hollow cylinder = π h (R² - r²)