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?

Correct answer:

p =  52.3599 %

Step-by-step explanation:

$$\begin{gathered} a=6\text{ m } \\ r=a\mathrm{/}2=6\mathrm{/}2=3\text{ m } \\ {V}_1=4\mathrm{/}3\pi \cdot r^3=4\mathrm{/}3\cdot 3.1416\cdot 3^3\doteq 113.0973{\text{m}}^3 \\ {V}_2=a^3=6^3=216{\text{m}}^3 \\ p=100\cdot V_1\mathrm{/}{V}_2=100\cdot 113.0973\mathrm{/}216=52.3599\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Inscribed sphere
  How many percent of the cube volume takes the sphere inscribed into it?
• 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?
• 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?
• 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?
• Reduce of the volume
  Calculate how many % reduce the volume of the cube is we reduced length of each edge by 10%.
• Cube zoom
  How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
• The cube
  The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
• Inscribed
  Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
• Cube in sphere
  The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
• Cube cut
  In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
• Cube edges
  If the edge length of the cube increases by 50%, how does the volume of this cube increase?
• Cube, cuboid, and sphere
  Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. At what rate are the volumes of cube, cuboid, and sphere?
• Cube into sphere
  The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
• Lathe
  Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
• Sphere radius
  The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
• Sphere area
  A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere.
• How many 9
  How many percent volume remain of a sphere if diameter decrease 3×?