Question

The base diameter of a metallic cylinder is 18cm and its height is 24 cm. It is melted into cylinders of base diameter 12 cm and height 6 cm. How many such small cylinders are formed?

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C

9

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

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

Let the number of new cylinders cast = 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 cast = 9