Question
A solid rectangular block of dimensions 4.4m, 2.6m and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness 5cm. Find the length of the pipe.
✓
Answer
We have,
Length of the rectangular block, l = 4. 4m,
Breadth of the rectangular block, b = 2. 6m,
Height of the rectangular block, h = 1m,
Internal radius of the cylindrical pipe, r = 30cm = 0. 3m and
Thickness of the pipe = 5cm = 0. 05m
Also, the external radius of the pipe = 0. 3 + 0. 05 = 0. 35m
Let the length of the pipe be H.
Now,
Volume of the pipe = Volume of the block
$\Rightarrow\pi\text{R}^2\text{H}=\pi\text{r}^2\text{H}=\text{lbh}$
$\Rightarrow\pi(\text{R}^2-\text{r}^2)\text{H}=\text{lbh}$
$\Rightarrow\frac{22}{7}\times(0.35^2-0.3^2)\text{H}=4.4\times2.6\times1$
$\Rightarrow\frac{22}{7}\times(0.1225-0.09)\text{H}=4.4\times2.6$
$\Rightarrow\frac{22}{7}\times0.0325\times\text{H}=4.4\times2.6$
$=\text{H}=\frac{4.4\times2.6\times7}{22\times0.0325}$
$\therefore\text{H}=112\text{m}$
So, the length of the pipe is 112m.
Length of the rectangular block, l = 4. 4m,
Breadth of the rectangular block, b = 2. 6m,
Height of the rectangular block, h = 1m,
Internal radius of the cylindrical pipe, r = 30cm = 0. 3m and
Thickness of the pipe = 5cm = 0. 05m
Also, the external radius of the pipe = 0. 3 + 0. 05 = 0. 35m
Let the length of the pipe be H.
Now,
Volume of the pipe = Volume of the block
$\Rightarrow\pi\text{R}^2\text{H}=\pi\text{r}^2\text{H}=\text{lbh}$
$\Rightarrow\pi(\text{R}^2-\text{r}^2)\text{H}=\text{lbh}$
$\Rightarrow\frac{22}{7}\times(0.35^2-0.3^2)\text{H}=4.4\times2.6\times1$
$\Rightarrow\frac{22}{7}\times(0.1225-0.09)\text{H}=4.4\times2.6$
$\Rightarrow\frac{22}{7}\times0.0325\times\text{H}=4.4\times2.6$
$=\text{H}=\frac{4.4\times2.6\times7}{22\times0.0325}$
$\therefore\text{H}=112\text{m}$
So, the length of the pipe is 112m.
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