Question

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is ______.

विकल्प

• 2 cm

• 3 cm

• 4 cm

• 6 cm

Answer 1

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is 2 cm.

Explanation:

Let the diameter of each sphere be d cm.

Let r and R be the radii of the sphere and the cylinder, respectively, and h be the height of the cylinder.

As R = `"Diameter"/2.`

`"R" = 2/2  "cm" = 1 " cm"`

h = 16 cm

Therefore, 

`=> 12 × 4/3xxpi"r"^3 = pi"R"^2"h"`

`=>12xx4/3"r"^3 = "R"^2"h"`

`=> 12xx4/3("d"/2)^3 = (1)^2 xx 16`

`=> 16xx"d"^3/8 = 16`

⇒ d³ = 8

⇒ d = ± 2

since d cannot of each sphere is 2 cm.

Hence, the diameter of each sphere is 2 cm.