Question

Ques .A solid sphere of metal with diameter 20 cm. is melted and poured into a cylindrical vessel with diameter 30 cm. To what hieght in cm will metal rise in vessel?
Pls explain

Answer 1

Height of Cylinder is 6 cm

Step-by-step explanation:

We know that,

Volume of Sphere = $\frac{4}{3}\times\pi \times R^3$

Volume of Cylinder = $\pi\times r^2 \times h$

where, h is height of cylinder,

R is Radius of Sphere and r is radius of cylinder

Here, radius of Sphere (R) = 10 cm (Half of Diameter 10 cm)

Radius of Cylinder (r) = 15 cm (Half of Diameter 30 cm)

According to Question,

Volume of Sphere = Volume of Cylinder

So, $\frac{4}{3}\times\pi \times R^3 = \pi\times r^2 \times h$

Removing the same terms from both sides-

$\frac {4}{3}\times10\times10\times10 = 15\times 15 \times h$

Which gives -

h = $\frac{160}{27}$

or h = 5.92 or 6 (Approx)

Hence, Height of Cylinder is 6 cm (Approx)