Question

A+metallic+cylinder+of+diameter+5cm.+And+height+3+1/3cm.is+melted+and+cast+into+a+sphere.+What+is+its+diameter.

Answer 1

Answer:

5 cm

Step-by-step explanation:

Given, diameter of metallic cylinder = 5cm

So, radius of its base = 5/2 = 2.5 cm

Its height = 3 1/3 cm (mixed fraction)

$= \frac{10}{3} \: cm$

So, volume of cylinder = πr²h

Taking π as 22/7, we get

Volume = 22/7 × 2.5 × 2.5 × 10/3

→ volume = 1375/21 cm³

Now, it is recasted into a sphere. Since, it is recasted, the volume of sphere will remain the same. Hence,

volume of sphere = 1375/21 cm³

We know that, volume of sphere = 4/3 × πr³

So, 4/3 × πr³ = 1375/21

Again, taking π as 22/7 we get

4/3 × 22/7 × r³ = 1375/21

→ 88/21 × r³ = 1375/21

→ r³= 1375/21 × 21/88

→ r³ = 15.625

→ r = ∛15.625

→ r = 2.5 cm

→ diameter = 2r = 2 × 2.5 = 5 cm