Inscribed

Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.

Correct result:

V =  523.5988 cm³

Solution:

$$\begin{gathered} a=10\text{ cm } \\ r=a\mathrm{/}2=10\mathrm{/}2=5\text{ cm } \\ V={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 5^3=523.5988{\text{cm}}^3 \end{gathered}$$

Try another example

Showing 0 comments:

Related math problems and questions:

• Cube into cylinder
  If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
• Pool
  The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
• Special body
  Above each wall of a cube with an edge a = 30 cm, a regular quadrilateral pyramid with a height of 15 cm is constructed. Find the volume of the resulting body.
• 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?
• Three cubes
  Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?
• Two rectangular boxes
  Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
• Cube in sphere
  The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
• For thinkings
  The glass cube dive into the aquarium, which has a length of 25 cm, width 20 cm and height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
• Cylinder in cube
  Into a paper box in the shape of a cube with an edge of 10 cm is placed a can in the shape of a cylinder with a height of 10 cm and touching all the walls of the cube. What % of the volume of the cube does the can take up?
• Cube walls
  Find the volume and the surface area of the cube if the area of one of its walls is 40 cm².
• 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.
• Cuboids in cube
  How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
• The body
  The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
• Cubes
  Most how many cubes with an edge length of 5 cm may fit in the cube with the inner edge of 0.4 m?
• Water level
  The glass container has a cuboid shape with dimensions of the bottom 24 cm and 12 cm. The height of the water is 26 cm. Calculate the body's volume, which is sunk into the water if the water level rise by 3 cm.
• Prism
  Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
• Cube surfce2volume
  Calculate the volume of the cube if its surface is 150 cm².