Question

a spherical ball of radius 10 cm is cut into 4 equal parts what is the total area of the parts​

Answer 1

❏ Question:-

A spherical ball of radius 10 cm is cut into 4 equal parts what is the total area of the parts ?

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❏ Solution:-

✦ FOR The LArge Sphere ✦

$\setlength{\unitlength}{1 cm}\begin{picture}(12,6)\thicklines\put(7.5,7.5){\circle{4}}\put(7.5,7.5){\line(1,0){0.70}}\put(4.2,8.5){ . }\put(7.2,7.6){ 10\:cm }\end{picture}$

➝ Volume of the Large Sphere,

$\sf\implies V_{\red{Large\: sphere}}=(\frac{4}{3}\pi \times 10^2)\:cm^3$

✦ FOR The Small Sphere ✦

$\setlength{\unitlength}{0.9cm}\begin{picture}(12,6)\thicklines\put(2,4){\circle{1}}\put(4,4){\circle{1}}\put(6,4){\circle{1}}\put(8,4){\circle{1}}\put(2.14,4.1){ r }\put(2,4){\line(1,0){0.47}}\put(4.14,4.1){ r }\put(4,4){\line(1,0){0.47}}\put(6.14,4.1){ r }\put(6,4){\line(1,0){0.47}}\put(8.14,4.1){ r }\put(8,4){\line(1,0){0.47}}\end{picture}$

Let, the radius of each small sphere is = r cm.

$\therefore$ Volume of each small sphere is

$\sf\implies V_{\red{Small\: sphere}}=(\frac{4}{3}\pi \times r^2)\:cm^3$

$\therefore$ Volume of 4 such small spheres is

$\sf\implies V_{\red{Small\: sphere}}=4\times(\frac{4}{3}\pi \times r^2)\:cm^3$

Now, all these 4 spheres are made from the large sphere, so the volume will remain same in this case ,

$\therefore (\frac{4}{3}\pi \times 10^2)= 4\times(\frac{4}{3}\pi \times r^2)$

$\therefore 10^2= 4\times r^2)$

$\therefore r^2=\frac{\cancel{100}}{\cancel5}$

$\therefore r=\sqrt{25}$

$\therefore\boxed{\large{\red{r\:=\:5 \:cm}}}$

∴ Radius of each small Sphere = 5 cm.

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