Question

A slab, \[8\] inches long, \[11\] inches wide & \[2\] inches thick is melted and solidified in the form of a rod of diameter \[8\] inches. What is the length of the rod in inches?

Answer 1

Hint:In such a type of question volume of \[2\] shapes after solidification is the same. So we simply have to find out the volume of slab from given data. Then have to assume a height of rod and then make the equation for volume. Then equating the two values we can get the height of the rod.


Complete step by step solution:
As we know the volume of slab before and after melting is the same. So the volume of the rod will also be the same as the volume of slab.
We know, length of slab \[ = {\text{ }}8{\text{ }}inch\],
Width of slab \[ = {\text{ }}11{\text{ }}inch\]and thickness of slab \[ = {\text{ }}2{\text{ }}inch\]
So the volume of slab \[ = {\text{ }}length{\text{ }} \times {\text{ }}width{\text{ }} \times {\text{ }}thickness\]
Volume of slab $ = 8 \times 11 \times 2$cubic inch
     $ = 176{\text{ cubic inch }}...{\text{(1)}}$
Radius of the rod is \[4\] inches and let us assume the length of rod is \[h\] .
Diameter of rod is \[8\] inch
Then the volume of the rod $ = \pi \times 4 \times 4 \times h{\text{ }}...{\text{(2)}}$ cubic inch
As the volume of slab and volume of rod is same, equating these two equations we get,
$176 = \pi \times 4 \times 4 \times h$
$176 = \dfrac{{22}}{7} \times 4 \times 4 \times h$
$\dfrac{{176 \times 7}}{{22 \times 4 \times 4}} = h$
$h = 3.5{\text{ inch}}$
So the length of the rod is \[3.5{\text{ }}inch\].


Note: As the slab is being melted and then solidification is done in form of rod, so the volume is remaining unchanged. Volume of cuboid is equal to volume of cylinder and height of rod is assumed to form the volume equation, on putting various parameter’s values which are given we can get height of rod. Here we have to be conscious where the diameter or radius of rod is given to us. If diameter is given then we have to apply the formula for volume accordingly and vice versa.