Answer:
Surface area of the cube = 216 square units
Step-by-step explanation:
Let the length of a side of a cube = x unit
Diameter of the sphere inscribed in this cube = length of a side of the cube
Volume of the sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]
Where r = radius of the sphere = [tex]\frac{x}{2}[/tex] units
36π = [tex]\frac{4}{3}\pi (\frac{x}{2})^{3}[/tex]
36π = [tex]\frac{4x^{3}\pi }{24}[/tex]
36×24 = 4x³
x = [tex]\sqrt[3]{\frac{36\times 24}{4} }[/tex]
x = 6 units
Length of a side of the cube = 6 units
Surface area of the cube = 6×(Side)²
= 6×(6)²
= 216
= 216 square units
