A slab of ice 8 inches in length, 11 inches in breadth and 2 inches thick was melted and resolidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to
- 3
- 3.5
- 4
- 4.5
- 2.5
The Correct Option is B
Solution and Explanation
To solve the problem, we need to find the length of a rod formed from a melted slab of ice, given that the diameter of the rod is 8 inches.
First, we calculate the volume of the original ice slab. The formula to find the volume of a cuboid (slab) is:
\(V = \text{length} \times \text{breadth} \times \text{height}\)
The dimensions of the slab are length = 8 inches, breadth = 11 inches, and height = 2 inches. Substituting these values into the formula gives:
\(V = 8 \times 11 \times 2 = 176 \text{ cubic inches}\)
Next, we need to find the volume of the cylindrical rod formed from this melted ice. The volume of a cylinder is given by the formula:
\(V = \pi r^2 h\)
where \(r\) is the radius of the base and \(h\) is the height (length) of the cylinder.
Given the diameter of the rod is 8 inches, the radius \(r\) is half of that, so:
\(r = \frac{8}{2} = 4 \text{ inches}\)
Since the volume of the rod is the same as the volume of the slab, we equate the two volumes:
\(\pi r^2 h = 176\)
Substituting the values of \(r\):
\(\pi (4)^2 h = 176\)
\(\pi \times 16 \times h = 176\)
Solve for \(h\):
\(h = \frac{176}{16\pi}\)
Using the value of \(\pi \approx 3.14159\), calculate \(h\):
\(h \approx \frac{176}{16 \times 3.14159} \approx 3.5 \text{ inches}\)
Thus, the length of the rod is approximately 3.5 inches.
Therefore, the nearest option is: 3.5
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