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

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

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

## What size box maximizes volume?

You’ve got your answer: a height of 5 inches produces the box with maximum volume (2000 cubic inches). Because the length and width equal 30 – 2h, a height of 5 inches gives a length and width of 30 – 2 · 5, or 20 inches. Thus, the dimensions of the desired box are 5 inches by 20 inches by 20 inches.

What is volume of a rectangle?

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

How do you find maximum volume using differentiation?

You can find the maximum of the volume by first finding the critical points of this function by finding the first derivative, then evaluating the second derivative at the critical points. If the second derivative is negative, that critical point is a maximum.

### How do you find the maximum and minimum volume?

To find the maximum possible area, add the greatest possible error to each measurement, then multiply. To find the minimum possible area, subtract the greatest possible error from each measurement, then multiply.

### 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 maximum volume of a gas?

Calculating the volume of a gas

1. Volume = amount in mol × molar volume.
2. Volume = 0.25 × 24.
3. = 6 dm 3

How do you find the volume of a rectangular box?

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.