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”.