Question

22 solid metallic cubes of side 4 cm are melted and 16 equal solid cylinders of height 7 cm are formed. Find the radius (in cm) of the cylinders so formed. (\(\pi=\frac{22}{7}\))

• A. 1.5
• B. 2
• C. 2.4
• D. 2.5

Hint:

Volume remains constant during melting

Answer 1

The Correct Option is B

Step 1: Compute volume of one cube.
Side of cube = 4 cm.
Volume of one cube = \(4^3 = 64\) cm³. Step 2: Compute total volume of all cubes.
Number of cubes = 22.
Total volume = \(22 \times 64 = 1408\) cm³. Step 3: Write volume formula for one cylinder.
Height of cylinder \(h = 7\) cm.
Radius = \(r\) cm (to be found).
Volume of one cylinder = \(\pi r^2 h = \frac{22}{7} \times r^2 \times 7\). Step 4: Simplify volume of one cylinder.
\(\frac{22}{7} \times 7 = 22\).
Thus, volume of one cylinder = \(22 r^2\) cm³. Step 5: Compute total volume of all cylinders.
Number of cylinders = 16.
Total cylinder volume = \(16 \times 22 r^2 = 352 r^2\) cm³. Step 6: Apply volume conservation (melting).
Total volume of cubes = Total volume of cylinders.
\(352 r^2 = 1408\). Step 7: Solve for \(r^2\).
\(r^2 = \frac{1408}{352}\).
Divide numerator and denominator by 352: \(1408 \div 352 = 4\).
So \(r^2 = 4\). Step 8: Solve for \(r\).
\(r = \sqrt{4} = 2\) cm (radius is positive).