# How do you find the diagonal length of a rectangular box?

Table of Contents

- 1 How do you find the diagonal length of a rectangular box?
- 2 What is the maximum possible volume of a rectangular box that can be inscribed in the unit sphere?
- 3 How do you find the maximum volume of a rectangular box with the surface area?
- 4 What is the volume of a box?
- 5 How many diagonals are in a rectangle?
- 6 Is the diagonal of a rectangle equal to its length?

## How do you find the diagonal length of a rectangular box?

You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w² , and now you should know how to find the diagonal of a rectangle explicit formula – just take a square root: d = √(l² + w²) .

## What is the maximum possible volume of a rectangular box that can be inscribed in the unit sphere?

8r3/3√3

Hence, the maximal volume of a rectangular box inside the sphere is 8r3/3√3.

**What is the formula to find diagonal?**

The formula to find the number of diagonals is n(n – 3)/2, where n is the number of sides the polygon has. If l, b and h denote the length, breadth and height respectively of the cuboid then the length of its diagonal d is given by the formula d = √(l^2+b^2+h^2).

### How do you find the maximum volume of a rectangular box with the surface area?

For a closed rectangular box with a total surface area of 64 square units, the maximum volume will be contained in a cube. Each of the six square faces will have an area of 64/6 square units and the side length will be the square root of the area, (4*6^0.5)/3. Cube that to get the volume.

### What is the volume of a box?

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 is the diagonal of a rectangular?**

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

#### How many diagonals are in a rectangle?

two diagonals

Rectangles have two diagonals that connect two opposite vertices. They are the same size.

#### Is the diagonal of a rectangle equal to its length?

A rectangle has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. The diagonals have the following properties: The two diagonals are congruent (same length).