Question

If a solid sphere of radius 10cm is moulded into 8 spherical solo balls of equal radius, then the surface area of each ball

Answer 1

$volume \: of \: each \: small \: ball = \frac{volume \: of \: sphere}{8} \\ \frac{4\pi {r}^{3} }{3} = \frac{4\pi {10}^{3} }{8 \times 3} \\ {r}^{3 } = { (\frac{10}{2} )}^{3} \\ r = 5cm \\ surface \: area \: of \: each \: ball = 4\pi \: {r}^{2} \\ = 4 \times \frac{22}{7} \times 5 \times 5 \\ = \frac{2200}{7} = 3.14 \times 100 = 314 {cm}^{2}$

Answer 2

Answer:

$314 cm^2$  

Step-by-step explanation:

Radius of big sphere = 10 cm

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

                                     =$\frac{4}{3} \times 3.14 \times 10^3$

                                     =$4186.66666667$

Since we are given that this big sphere is recast into 8 identical spherical balls of same radius.

So, Volume of big sphere = Volume of 8 spheres

So, Volume of 1 Spherical ball = $\frac{4186.66666667}{8}$

                                                   = $523.333333334$

Volume of spherical ball =$\frac{4}{3}\pi r^3$

So,  $523.333333334=\frac{4}{3} \times 3.14 r^3$

        $\frac{523.333333334}{\frac{4}{3} \times 3.14}= r^3$                

        $125= r^3$                        

        $\sqrt{3}{125}= r$            

        $5= r$                                          

Surface area of each ball = $4 \pi r^2$  

                                           = $4 \times 3.14 \times (5)^2$  

                                           = $314 cm^2$  

Hence  the surface area of each ball is  $314 cm^2$