# How do you find the volume of a cube inscribed in a sphere?

## How do you find the volume of a cube inscribed in a sphere?

Formula. Four thirds pi r cubed is four thirds pi 15 cubed i’ll get out my calculator.

### How do you find the side length of a cube inscribed in a sphere?

When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere. Since the sphere has a radius of 6 and a diameter of 12, you know that the sphere has a long diagonal of 12. The long diagonal of a cube is related to a side of the cube using the formula d = s .

#### How do you find the surface area of a sphere inscribed in a cube?

The side of the cube is the same as the diameter of the sphere. Since d = 4, r = 2. The surface area of a sphere is found by SA = 4π(r2) = 4π(22) = 16π.

What percentage of a cube is a sphere?

For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of the cube, since V = π/6 d3, where d is the diameter of the sphere and also the length of a side of the cube and π/6 ≈ 0.5236.

How do you find the volume of a cube given the radius?

Volume of a Cube – MathHelp.com – Math Help – YouTube

## What is the cube formula?

x 3 = x × x × x. In algebra, cube refers to a number raised to the power 3. However, the meaning of cube is different in geometry, i.e. cube is a 3d shape with equal measure of edges and all the faces are squares.

### What is the total surface area of a cube that is inscribed in a sphere of radius 8 cm?

= 864 square cm.

#### What is the formula of inscribed circle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa2/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

How many cube does a sphere have?

For example:

Solid Shapes Faces Vertices
Sphere 1 0
Cylinder 3 0
Cone 2 1
Cube 6 8

How many spheres fill a cube?

These two layer configurations are then repeated until there are 71 configurations like the first layer, and 70 like the second layer. This gives a total of 71×9941+70×9940=1401611 balls.

## How do I calculate volume of a cube?

The volume of a cube is obtained by multiplying its side three times. The formula of volume of the cube can thus be given as, Volume of cube = s3, where s is the side length of the cube.

### What is the formula of finding the volume of a cube?

The formula of volume of the cube is given by: Volume = a3, where a is the length of its sides or edges.

#### Is the cube of 1?

The cube root of 1 is the number which when multiplied by itself three times gives the product as 1. In fact, the n-th root of 1 is always 1. Therefore, the cube root of 1 = ∛1 = 1.

How do u find volume of a cube?

What is the formula of cube?

However, the meaning of cube is different in geometry, i.e. cube is a 3d shape with equal measure of edges and all the faces are squares. Based on this, we can also write the volume of cube formula since cube has equal length, breadth and height. Therefore, the volume of cube formula is a × a × a = a3.

## What is the formula for inscribed circle?

Then the radius r of its inscribed circle is r=Ks=√s(s−a)(s−b)(s−c)s. Recall from geometry how to bisect an angle: use a compass centered at the vertex to draw an arc that intersects the sides of the angle at two points.

### How do you calculate inscribed?

The measure of an inscribed angle is equal to half the measure of the central angle that goes with the intercepted arc. The measure of an inscribed angle is equal to half the measure of its intercepted arc.

#### How do you solve inscribed?

Inscribed Angles – MathHelp.com – Geometry Help – YouTube

Do you cube the volume of a sphere?

The volume V of a sphere is four-thirds times pi times the radius cubed. The volume of a hemisphere is one-half the volume of the related sphere. Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

Does a sphere have 3 faces?

Faces. A face is a flat or curved surface on a 3D shape. For example a cube has six faces, a cylinder has three and a sphere has just one.

## How do you calculate spheres?

The formula for the volume of a sphere is V = 4/3 πr³. See the formula used in an example where we are given the diameter of the sphere. Created by Sal Khan and Monterey Institute for Technology and Education.

### How many cubic inches is a 1 inch sphere?

One one-inch diameter sphere in volume and capacity sense converted to cubic inches equals precisely to 0.52 cu in – in3.

#### What is a formula for the volume of a sphere?

What is the volume of a cube 3x3x3?

27 cubic inches
Therefore the volume of the cube is 3 in x 3 in x 3 in = 27 cubic inches.

Is the number 1 a perfect cube?

The numbers such as 1, 8, 27, 64, etc. are known as perfect cubes or cube numbers. When a cube is broken or cut, total volume still remains the same.