Question

A solid rectangular block of dimensions 2.2 metre into 1.2 metre into one is cost cast into a hollow cylindrical pipe of internal radius 7 by 2 cm and thickness 5 cm find the length of the pipe

Answer 1

SOLUTION:-

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Given:

A solid rectangular block of dimensions 2.2m × 1.2m × 1m is cast into a hollow cylindrical pipe of internal radius 7/2 cm & thickness 5cm.

To find:

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The length of the pipe.

Explanation:

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• The dimensions of the rectangular block is 2.2m × 1.2m ×1m.

The volume of the rectangular block;

{length×breadth× height} cubic units.

Therefore,

• Length,(l)=2.2m
• Breadth,(b)=1.2m
• Height,(h)= 1m

Volume= [2.2 ×1.2 ×1]m³

Volume= [2.64]m³.............(1)

Assume the internal radius of the hollow cylindrical pipe be r= 7/2cm

{In meters= 3.5/100}= 0.035m.

•The thickness= 5cm

In metres= 0.05m

Assume the external radius of the pipe be R= r+0.05

=) 0.035m + 0.05m

=) 0.085m

Let the length of the pipe be h m.

Now,

The volume of the pipe:

π(R² -r²)h

$= > \frac{22}{7} (0.085 {}^{2} - 0.035 {}^{2} )h.................(2)$

The volume of the pipe= volume of the rectangular block.

Eq (1)= Eq(2), we get;

$= > \frac{22}{7} (0.085 {}^{2} - 0.035 {}^{2} ) \times h = 2.64 \\ \\ = > \frac{22}{7} (0.007225 - 0.001225)h = 2.64 \\ \\ = > \frac{22}{7} \times 0.006 \times h = 2.64 \\ \\ = > h = \frac{2.64 \times 7}{22 \times 0.006} \\ \\ = > h = \frac{18.48}{0.132} m \\ \\ = > h = \frac{18.48 \times 1000}{0.132 \times 1000} m \\ \\ = > h = \frac{18480}{132} m \\ \\ = > h = 140m$

Thus,

The length of the pipe is 140m.

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