Question

A slab of ice $8$ inches in length, $11$ inches in breadth, and $2$ inches thick was melted and resolidified in the form of a rod of $8$ inches diameter. What is the length of such a rod in inches?

• A. $3.5$ inches
• B. $4.5$ inches
• C. $5$ inches
• D. $4$ inches

Answer 1

Answer: (A)

$3.5$ inches

The slab of ice is in the shape of a cuboid.

Volume of a cuboid $=l\times b\times h$

Volume of the ice $=8\times 11\times 2=176$ inches${}^3$

The rod is in the shape of a cylinder.

Volume of a Cylinder $=\pi R^{2}h$

Radius of the rod $=\frac{Diameter}{2}=4$ inches

=> Volume of the rod of ice $=\pi \times 4^2\times h=16\pi h$

Volume of cuboidal ice will be equal to the volume of rod of ice

$=>176=16\pi h$

$=>h=\frac{176\times 7}{16\times 22}=3.5$ inches.