Table of Contents

- 1 What is the change in the volume of cube if the edge is doubled?
- 2 What will happen to the volume of a cube if its edge is doubled and halved?
- 3 What happens to the surface area of a cube if the length of each side is tripled?
- 4 What happens to the volume of a cube when its edge is tripled?
- 5 What is the formula for doubling a cube?
- 6 Why is a cube of side length 1 not a number?

## What is the change in the volume of cube if the edge is doubled?

Thus, the obtained volume with the edge being doubled is equal to 8 times the volume of a cube with edge x.

## What will happen to the volume of a cube if its edge is doubled and halved?

the volume will increase 8 times. if edge is halved, therefore, therefore, the original volume will 8 times less of the new volume.

**What will happen to the volume of cube if its edge is tripled?**

It’s volume is increased 27 times.

**What will happen to the volume of cube?**

the answer is “the volume would be 1/8 th of the original volume”.

### What happens to the surface area of a cube if the length of each side is tripled?

Similarly when length is tripled (x = 3) surface area is increased ninefold (32 = 9) and volume is increased twenty-sevenfold (33 = 27).

### What happens to the volume of a cube when its edge is tripled?

=volume will increase 27 times.

**What effect will Doubling the radius and halving the height of a cylinder have on its volume?**

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

**Can you construct a second cube whose volume is double the first?**

Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first.

## What is the formula for doubling a cube?

In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x³ = 2; in other words, x = ³√2. This is because a cube of side length 1 has a volume of 1³ = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.

## Why is a cube of side length 1 not a number?

This is because a cube of side length 1 has a volume of 1³ = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that “³√2 is not a constructible number”.