Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste.

Correct answer:

p =  47.6401 %

Step-by-step explanation:

$$\begin{gathered} a=1 \\ r=a\mathrm{/}2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ {V}_1=a^3=1^3=1 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 0.5^3\doteq 0.5236 \\ p=100\cdot {\displaystyle \frac{V_1-V_2}{V_1}}=100\cdot {\displaystyle \frac{1-0.5236}{1}}=47.6401\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Cube in a sphere
  The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube.
• Cube in ball
  Cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere?
• Cube in sphere
  The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the volume of the cube from the volume of the ball?
• Cube diagonals
  Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
• Body diagonal
  Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
• Body diagonal - cube
  Calculate the surface and cube volume with body diagonal 15 cm long.
• Sphere vs cube
  How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
• Inscribed sphere
  How many percent of the cube volume takes the sphere inscribed into it?
• Cube wall
  Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume.
• Body diagonal
  Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• Cube and sphere
  Cube with the surface area 150 cm² is described sphere. What is sphere surface?
• Inscribed sphere
  How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
• Sphere area
  A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
• Cube diagonals
  Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.
• Cube wall
  The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
• Surface and volume - cube
  Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• Cube diagonal
  Determine the length of the cube diagonal with edge 37 mm.