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

Question

There are five dustbins along a circular path at different places. Ramesh takes multiple rounds of the path every morning, always at the same speed. He noticed that it took him a different number of steps to walk between any two consecutive dustbins. Ramesh also noticed that starting from any of the dustbins, it took a minimum 360 steps to reach every second dustbin, and a maximum 1260 steps to reach every third dustbin. If Ramesh's step size is 0.77 meter, and the width of the path is negligible, which of the following can be the radius of the circular path?

Answer 1

The correct answer is option (B):

3.5

Here's how to solve this problem:

1. Calculate the volume of the ice slab:
* Volume = length x breadth x thickness
* Volume = 8 inches x 11 inches x 2 inches = 176 cubic inches

2. Understand that melting and resolidifying doesn't change the volume. The volume of the ice slab is equal to the volume of the rod.

3. Calculate the volume of the rod using the formula for the volume of a cylinder:
* Volume of a cylinder = π * radius² * length
* We know the diameter of the rod is 8 inches, so the radius is 8 inches / 2 = 4 inches.
* Let 'l' be the length of the rod.
* 176 cubic inches = π * (4 inches)² * l

4. Solve for the length (l):
* 176 = π * 16 * l
* l = 176 / (16π)
* l ≈ 176 / (16 * 3.14) (Using π ≈ 3.14)
* l ≈ 176 / 50.24
* l ≈ 3.5 inches

Therefore, the length of the rod is nearest to 3.5 inches.

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

The Correct Option is B

Solution and Explanation

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