What is the volume of a box that can be inscribed in a sphere of unit radius?
What is the volume of a box that can be inscribed in a sphere of unit radius?
Summary: The maximal volume of the rectangle inside the sphere of radius r and that volume is 8r3/3√3.
What is the formula of volume of the cube?
Volume of Cube = √3 × d3/9 Hence, by measuring the length of the diagonal of cube, we can evaluate the volume of cube. Example: If length of diagonal of cube is 3 inches, then the volume will be: Volume = √3 × d3/9 = √3 × 33/9 = 3√3 cu.in.
What is the volume of the sphere?
V = 4/3 πr³
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.
When a cube is 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 .
What is the equation for a sphere?
The general equation of the sphere is x2 + y2 + z2 = r2 and in this article, we will learn about deriving the equation of a sphere along with its volume and surface area.
Why is it 4 3 for volume of a sphere?
Volume of a sphere = 4/3 πr3 If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.
How do you solve for volume?
To find the volume of a box, simply multiply length, width, and height — and you’re good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.
What will be the ratio of volume of cube is to volume of sphere inscribed in the cube?
6 : π
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.