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3 years ago

If the volume of a sphere inscribed in a cubic box is 36pi, find the surface area of the box

Mathematics

1 answer:

Kruka [31]3 years ago

3 0

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 = $\frac{4}{3}\pi r^{3}$

Where r = radius of the sphere = $\frac{x}{2}$ units

36π = $\frac{4}{3}\pi (\frac{x}{2})^{3}$

36π = $\frac{4x^{3}\pi }{24}$

36×24 = 4x³

x = $\sqrt[3]{\frac{36\times 24}{4} }$

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

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