Question

1 cm and 6 cm in diameter Determine the outer radius of the new sphere by melting two solid spheres with a radius to form a 1 cm thick hollow sphere.

Answer 1

Answer:

If two solid spheres of radii 1 cm and 6cm are melted to form a hollow sphere of thickness 1 cm, then what will be the surface area of hollow sphere?

The volume of sphere 1 = (4/3)(22/7)*1^3 =(88/21)*1 cc

The volume of sphere 2 = (4/3)(22/7)*6^3 =(88/21)*216 cc.

The combined volume of the two spheres = (88/21)*217 cc.

The hollow sphere has an outer radius of x and the internal radius = (x-1).

Volume of the hollow sphere = (4/3)(22/7)[x^3-(x-1)^3]= (88/21)[x^3-(x-1)^3] = (88/21)*217, or

[x^3-(x-1)^3] = 217, or

x^3-(x^3–3x^2+3x-1) = 217, or

x^3-x^3+3x^2-3x+1 = 217, or

3x^2–3x-216=0, or

x^2-x-72=0, or

(x-9)(x+8)=0, or

x = 9 as -8 has no meaning.

So the hollow sphere has a surface area of 4(pi)*9^2 = 1018.29 sq cm.