Question

a metallic cylinder of diameter 5cm and height 10/3cm is melted and cast into a sphere what is its diameter ​

Answer 1

Diameter of the metallic cylinder = 5 cm 

Radius = 5/2 = 2.5 cm

Height of the metallic cylinder = 10/3 cm

Volume of the metallic cylinder = πr²h

⇒ 22/7 × 2.5 × 2.5 × 10/3

⇒ 1375/21

⇒ 65.476 cm³

The metallic cylinder is melted and cast into a sphere. So, the volume of the metallic cylinder and the sphere will exactly same.

Volume of sphere = 4/3πr³

⇒ 65.476 = 4/3 × 22/7 × r³

⇒ 88 r³ = 65.476 × 21

⇒ 88 r³ = 1375 (Approx)

⇒ r³ = 1375/88

⇒ r³ = 15.625

⇒ r = ∛15.625

⇒ r = 2.5 

Hence, the radius of the sphere is 2.5 cm.

Then, diameter of the sphere = 2.5×2 = 5 cm

Hope it helps..

Answer 2

Radius of cylinder, r= 5/2 cm

Height of cylinder, h=10/3 cm

Volume=$\pi r^{2} h=\pi *(\frac{5}{2})^{2}*\frac{10}{3}=65$

Let radius of sphere be R

Volume of sphere=$\frac{4}{3} \pi R^{3} =65\\R=\sqrt[3]{\frac{65*3}{4\pi } } =2.5 cm$

Diameter of sphere = 2R = 5cm

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