Why is the volume of a box 8xyz?

Clearly the box will have the greatest volume if each of its corners touch the ellipse. Let one of the corners (x, y, z) be in the positive octant, then the box has corners (±x, ±y, ±z) and its volume is V = 8xyz.

How can you find the maximal volume of a rectangular box inscribed in a sphere?

Equations (4) and (5) are partial derivatives and have to be equated to zero to maximize the volume of the rectangular box. Hence, the maximal volume of a rectangular box inside the sphere is 8r3/3√3.

How do you find the maximum area of a rectangle?

Approach: For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).

How do you find the dimensions of a rectangular box that has the largest volume and surface area of 56 square units?

The maximum volume is 56√219≈28.5 cubic units. Let x , y , and z be the dimensions of the box. Then V=xyz and S=2xy+2xz+2yz are the volume and surface areas of the box.

How do you find the volume of a rectangular sphere?

The formula for the volume of a sphere is V = 4/3 πr³.

What is volume of rectangle?

The equation for calculating the volume of a rectangle is shown below: volume= length × width × height.

What is the volume of a rectangle calculator?

Volume of a Rectangle Calculator A Rectangular box is a geometrical figure bounded by six quadrilateral faces. The shape is also known as the rectangular cuboid, right cuboid, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped. The volume of a rectangular box is the amount of space occupied by the object.

What is the name of a rectangular box?

A Rectangular box is a geometrical figure bounded by six quadrilateral faces. The shape is also known as the rectangular cuboid, right cuboid, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped. The volume of a rectangular box is the amount of space occupied by the object.

How to calculate the volume of a box?

Then the volume of the box is 8 x y z. The sphere of radius a is given by x 2 + y 2 + z 2 = a 2. g ( x, y, z) = 0 where g ( x, y, z) = x 2 + y 2 + z 2 − a 2.

How many faces does a rectangular tank have?

A rectangular tank is a generalized form of a cube, where the sides can have varied lengths. It is bounded by six faces, three of which meet at its vertices, and all of which are perpendicular to their respective adjacent faces.