The diameter of a solid metallic sphere is 3.5 cm. Such 96 spheres are melted and recast into a solid right circular cylinder of height 56 cm.
What is the curved surface area (in cm²) of the cylinder?

Correct option is C

​Given :

Diameter of sphere = 3.5 cm

Radius r = 1.75 cm

Number of spheres = 96

Height of cylinder h = 56 cm

Formula Used :

Volume of sphere $$= \frac{4}{3}\pi r^3$$​​

Volume of cylinder =$$\pi R^2 h$$​​

Curved surface area of cylinder = $$2\pi R h$$​​

Solution :

Volume of one sphere

​$$\frac{4}{3}\pi (1.75)^3$$​​
​$$= \frac{4}{3}\pi \left(\frac{7}{4}\right)^3$$​​
=$$\frac{343\pi}{48}$$​​
Volume of 96 spheres

96$$\times \frac{343\pi}{48} = 2 \times 343\pi = 686\pi$$​​
Volume of cylinder

​$$\pi R^2 \times 56 = 686\pi$$​​

​$$R^2 = \frac{686}{56} = \frac{49}{4}$$​​
R = $$\frac{7}{2}$$​​
Curved surface area of cylinder

​$$2\pi R h = 2\pi \times \frac{7}{2} \times 56$$​​

= 7$$\times 56 \pi = 392\pi$$​​