Question

If a solid metallic hemisphere of radius 8 cm is melted and recast into x spheres of radius 2cm each, the x is equal to

Answer 1

The value of x is equal to 32.

Step-by-step explanation:

Given,

A solid metallic hemisphere of radius (r) = 8 cm and

the radius of sphere = 2 cm

To find, the value of x = ?

We know that,

The volume of hemisphere = $\dfrac{2}{3} \pi r^3$

and

The volume of sphere = $\dfrac{4}{3} \pi r^3$

According to  queston,

The volume of hemisphere = x (The volume of sphere)

∴ $\dfrac{2}{3} \pi 8^3=x\times \dfrac{4}{3} \pi 2^3$

⇒ $8^3=x\times 2\times 2^3$

⇒ 512 = x × 16

⇒ x = $\dfrac{512}{16}$

⇒ x = 32

Thus, the value of x is equal to 32.

Answer 2

Given,

A solid metallic hemisphere of radius (r) = 8 cm and

the radius of sphere = 2 cm

We know that,

To find, the value of x = ?

The volume of hemisphere = 2/3×πr^2

and

The volume of sphere = 4/3×πr^3

According to  question,

The volume of hemisphere = x (The volume of sphere)

2/3π×8×8×8=x×4/3×π×2×2×2

512=x×16

x=512/16

x=32