Question

circle
a) A metallic sphere of diameter 84 cm is melted and recast
into the shape of cube of side 2 cm. Find how many
cubes can made.​

Answer 1

Answer:

The volume of the solid sphere = sum of the volumes of n spherical balls. Therefore, 512 balls can be made of radius 1 cm each with a solid sphere of radius 8 cm. 2.

Answer 2

Number of cubes can made = 38772

Step-by-step explanation:

Volume of the solid sphere = Volumes of n cubes.

Let r be the radius of the solid sphere

Volume of the solid sphere = $\frac{4}{3} \pi r^{3}$

Therefore, r= $\frac{d}{2}$ where d is the diameter

So, r = $\frac{84}{2}$ cm = 42 cm

Let a be the side of the cube

Volume of cube = $a^{3}$

As Volume of the solid sphere = Volumes of n cubes

$\frac{4}{3} \pi r^{3}$= n $a^{3}$

Now $\frac{4}{3} \pi r^{3}$ = $\frac{4}{3} \pi 42^{3}$ = 310181 $cm^{3}$

$a^{3}$ = $2^{3}$ = 8 $cm^{3}$

Therefore, 310181 = 8n

⇒ n = 38772

Therefore number of cubes can made = 38772