A solid iron cuboidal block of dimensions 4.4 | vedclass

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Question

(A) Given that,a solid iron cuboidal block is recast into a hollow cylindrical pipe.Volume of the cuboidal block $= l 	imes b 	imes h = 4.4 \, m 	i

Vedclass · Accepted Answer

$112$

Vedclass · Answer

(A) Given that,a solid iron cuboidal block is recast into a hollow cylindrical pipe.Volume of the cuboidal block $= l 	imes b 	imes h = 4.4 \, m 	imes 2.6 \, m 	imes 1 \, m = 11.44 \, m^3$.Internal radius of the hollow cylindrical pipe $(r_i) = 30 \, cm = 0.3 \, m$.Thickness of the pipe $= 5 \, cm = 0.05 \, m$.External radius $(r_e) = r_i + 	ext{thickness} = 0.3 \, m + 0.05 \, m = 0.35 \, m$.Volume of the hollow cylindrical pipe $= \pi (r_e^2 - r_i^2) h_1$,where $h_1$ is the length of the pipe.Volume $= \frac{22}{7} 	imes (0.35^2 - 0.3^2) 	imes h_1 = \frac{22}{7} 	imes (0.1225 - 0.09) 	imes h_1 = \frac{22}{7} 	imes 0.0325 	imes h_1$.Since the volume remains constant: $11.44 = \frac{22}{7} 	imes 0.0325 	imes h_1$.$h_1 = \frac{11.44 	imes 7}{22 	imes 0.0325} = \frac{80.08}{0.715} = 112 \, m$.Thus,the length of the pipe is $112 \, m$.

Part $I$	Part $II$
$1.$ Volume of a cuboid	$a.$ $\frac{1}{3} \pi r^{2} h$
$2.$ Volume of a cone	$b.$ $\pi r^{2} h$
$3.$ Volume of a cylinder	$c.$ $\frac{4}{3} \pi r^{3}$
$4.$ Volume of a sphere	$d.$ $lbh$

$A$ solid iron cuboidal block of dimensions $4.4 \, m \times 2.6 \, m \times 1 \, m$ is recast into a hollow cylindrical pipe of internal radius $30 \, cm$ and thickness $5 \, cm$. Find the length of the pipe in meters.

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Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$ Part $II$

$1.$ Volume of a cuboid $a.$ $\frac{1}{3} \pi r^{2} h$

$2.$ Volume of a cone $b.$ $\pi r^{2} h$

$3.$ Volume of a cylinder $c.$ $\frac{4}{3} \pi r^{3}$

$4.$ Volume of a sphere $d.$ $lbh$

The volume of a hemisphere is equal to:

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