Question

A metallic cylinder of diameter 5cm and height 3 1/3cm and cast into a sphere.what is its diameter ​

Answer 1

solution:-

Given diameter of metallic cylinder=5 cm

So radius of cylinder=2.5 cm

And its height =

$3 \times \frac{1}{3} = \frac{10}{3} \sf{cm}$

Then volume of cylinder = πr²h=π×(2.5)²×$\dfrac{10}{3}$ cm³

Let radius of sphere is r

Then volume of sphere =$\dfrac{4}{3}$ πr³

Then volume of cylinder =volume of sphere

∴$\dfrac{4}{3}$πr³=π×2.5×2.5×$\dfrac{10}{3}$

➛$r {}^{3} = \frac{2.5 \times 2.5 \times 10}{4} = \frac{62.5}{4} = 15.625$

➛r=2.5cm

So diameter of sphere=2×2.5=5cm