Question

A solid metal sphere is melted and smaller spheres, all with the same radius, are formed. 20% of the material is lost in this process. The radius of each smaller sphere is the radius of the original sphere. If 20 litres of paint was needed to paint the original sphere, then how many litres of paint would be required to paint all the smaller spheres?

Answer 1

Answer:

Step-by-step explanation:I don't know ans

Answer 2

Answer:-

17.2 litres.

Step-by-step explanation:

In this question,

We have been given that

 A solid metal sphere is melted and small spheres with the same radius are formed.20% of material is lost in the process.radius of each smaller sphere is the radius of small sphere.20 litres of paint was needed to paint the original sphere.

We need to find the paint would be required to paint smaller spheres.

Let the radius of the original sphere be R

Therefore volume of sphere = $\frac{4}{3}\times \pi\times r^{3}$

Let the Volume of the original sphere be V

20% of the material is lost in the process of forming smaller spheres.

Volume of the remaining material = $V\ -\ \frac{1}{5}V$

                                                        = $\frac{4}{5}V$

Now, volume of the remaining material will be equal to volume of smaller spheres.Let radius of smaller sphere be r

Now, $\frac{4}{5}(\frac{4}{3}\times \pi\times R^{3})\ =\ \frac{4}{3}\pi r^{3}$

         $\frac{16}{15}\pi R^{3}\ =\ \frac{4}{3}\pi r^{3}$

         $\R\ =\ r(\frac{5}{4})^{\frac{1}{3}}$

We know that Surface area of cube is = $4\pi r^{2}$

Let amount of paint required for painting smaller blocks be x litres.

Surface area of cube will be equal to total amount of paint required.

Therefore.$4\pi R^{2}\ =\ 20$

Similarly $4\pi r^{2}\ =\ x$

Now,$\frac{4 \pi R^{2}}{4 \pi r^{2}}\ =\ \frac{20}{x}$

        Putting the value of R we get,

       $\frac{4\pi r^{2}}{(\frac{5}{4})^{\frac{2}{3}}{4 \pi r^{2}}}$ = $\frac{20}{x}$

       $(\frac{5}{4})^{\frac{2}{3}}\ =\ \frac{20}{x}$

       $1.16\ =\ \frac{20}{x}$

       x=17.2

17.2 litres of paint will be required