Question

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
(a)√3 cm
(b)2 cm
(c)3 cm
(d)4 cm

Answer 1

Answer:

The Diameter of sphere is 4 cm.

Among the given options option (d) 4 cm is the correct answer.

Step-by-step explanation:

Given :  

Number of spheres = 12

Height of a solid cylinder ,h = 2 m

Diameter of solid cylinder = 16 cm  

Radius of solid cylinder ,R = 16/2 = 8 cm  

 

Let the Radius of sphere be r

Volume of solid cylinder = 12 ×  Volume of sphere  

[Solid spheres are made from melting a solid cylinder]  

πR²h = 12 × 4/3πr³

R²h = 16r³

8² × 2 = 16r³

64 × 2 = 16r³

r³ = (64 × 2)/16

r³ = 4 × 2  

r³ = 8  

r = ³√8

r = 2 cm

Radius of sphere = 2 cm

Diameter of sphere = 2 × Radius = 2 × 2 = 4 cm

Hence, the Diameter of sphere is 4 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Given,

12 spheres of same size are made from a solid cylinder.

Diameter of the cylinder = 16cm

Radius of the cylinder = 16/2 = 8cm

Height of the cylinder = 2cm

Volume of Cylinder = 12 × volume of sphere

$\pi {r}^{2} h = 12 \times \frac{4}{3} \pi {r}^{3} \\ \\ \frac{22}{7} \times {8}^{2} \times 2 = 4 \times 4 \times \frac{22}{7} \times {r}^{3} \\ \\ \frac{22}{7} \times 64 \times 2 = 16 \times \frac{22}{7} \times {r}^{3} \\ \\ 128 = 16 \times {r}^{3} \\ \\ \frac{128}{16} = {r}^{3} \\ \\ {r}^{3} = 8 \\ \\ r = \sqrt[3]{8} \\ \\ r = 2$

Diameter = 2 × 2 = 4cm

Therefore, the diameter of each sphere is 4cm.