Question

The base diameter and height of a metallic solid cylinder are 18 cm and 24 cm respectively. If the cylinder is melted to form cylinders of base diameter 12 cm and height 6 cm, how many such small cylinders will be formed?

• A. 9

Answer 1

The correct option is A 9

Cylinder 1
Diameter = 18 cm
Hence Radius (R) = 9 cm
Height (H) = 24 cm

Cylinder 2 (recast)
Diameter = 12 cm
Hence Radius (r) = 6 cm
Height (h) = 6 cm

Let the number of new cylinders = n

Hence Volume of Cylinder 1 = $n\times VolumeofCylinder2$

$\pi R^{2}H=n\pi r^{2}h$

$\pi \times 9\times 9\times 24=n\times \pi \times 6\times 6\times 6$

n = $\frac{9\times 9\times 24}{6\times 6\times 6}$

n = 9

Number of new cylinders = 9