Science & Mathematics » Mathematics » What is the volume of the largest (shape) that can fit inside a (shape)?

What is the volume of the largest (shape) that can fit inside a (shape)?

for example, What is the volume of the biggest sphere that can fit in a cube with a volume of 216cm3

do i have to get the sides of the cube first? so it'll be 2 sq. of 54. what do i do next? i know the formula for the volumes of each shape... but i dont quite know how "fit this into this" questions work. thank you!

Yes, side of cube will be cube root of 216.

It volumes
So you firstly want the cube root of the cuboid's volume .

Then halve that to get the radius of the sphere.

Yes first calculate the sides of the cube. Then imagine how you would fit the largest possible sphere inside: The center of the sphere would be in the center of the cube, what would the radius of the sphere be in terms of the sides of the cube?

The sides of the cube are 6 cm by the way, because 6 * 6 * 6 = 216

find the length of each side of the cube. The length of the side will be the diameter of the sphere.Now you can calculate the volume.
This gives the length = 6cm. Radius of the sphere is 3 cm
Volume = 4 pi /3 3*3=36 pi. This is the volume.

Largest Shape


You can tackle this question in this way.

Considering your example question, it is relatively easy to solve it. You were right by saying that you ve to find the sides of the cube, which is approximately 6 cm.

Now, if you were to fit a sphere of maximum volume that can be fit inside that cube, it s diameter has to be equal to the sides of the cube.

Then you can find the radius of the sphere and then the volume by using 4/3.pi.r3

Hopefully that helped :)