# Pyramid in cube

In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid.

Correct result:

V =  576 dm3
S =  465.9938 dm2

#### Solution:

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• 9-gon pyramid
Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• 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.
• Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
• Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
• The cube
The cube has a surface area of 216 dm2. Calculate: a) the content of one wall, b) edge length, c) cube volume.
• Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
• Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
• Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?