A metallic cylinder ofdiameter 5cm, and height 3×1/3.is melted and ca

1.	A metallic cylinder ofdiameter 5cm, and height 3×1/3.is melted and cast into a sphereWhat is its diameter
Answer» Solution :- Diameter of the metallic cylinder = 5 cm Radius = 5/2 = 2.5 cm Height of the metallic cylinder = 3 1/3 cm = 10/3 cm Volume of the metallic cylinder =πr²h ⇒ 22/7×2.5×2.5×10/3 ⇒ 1375/21 Volume of the metallic cylinder = 65.476 cu cm 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 ⇒ 88r³ = 65.476×21 ⇒ 88r³ = 1374.996 or 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

A metallic cylinder ofdiameter 5cm, and height 3×1/3.is melted and cast into a sphereWhat is its diameter

Answer»

Solution :-

Diameter of the metallic cylinder = 5 cm

Radius = 5/2 = 2.5 cm

Height of the metallic cylinder = 3 1/3 cm = 10/3 cm

Volume of the metallic cylinder =πr²h

⇒ 22/7×2.5×2.5×10/3

⇒ 1375/21

Volume of the metallic cylinder = 65.476 cu cm

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

⇒ 88r³ = 65.476×21

⇒ 88r³ = 1374.996 or 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