if the height of a cylinder was tripled, but the area of the base remained the same, what would happen to the volume?

Question

a.  the volume would double

b.  the volume would be four times greater

c.  the volume would triple

d.  the volume would be nine times greater

Answer 1

The formula for the volume of a cylinder is:

 

V_cylinder = (area of the base) x height

 

The simplest method: make up numbers and see how the volume changes.

Let's say that cylinder 1 has a base area of 6 and a height of 10. Cylinder two would have a base area of 6 and a height of 20.

Plug the values and solve:

V₁ = 6x10 = 60
V₂ = 6x20 = 120

The volume has doubled.

 

When doing this method, avoid using 1 and 2 as numbers, as it can be impossible to see the effect of squaring vs. doubling these numbers. Try to use numbers greater than 3.

 

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A more formal method (if you have enough algebra)

 

The area of the base being a circle would be:

 

area of the base = πr², where π = "pi", and r = radius of the base.

 

Combining these two formulas, you get:

 

V_cylinder = πr²h, where π is "pi", r is the radius of the base, and h is the height of the cylinder.

 

Imagine two cylinders: cylinder 1 (original) and cylinder 2 (with twice the height).

 

V₁ = πr₁²h₁

 

V₂ = πr₂²h₂

 

We know that the area for V₂ does not change (so, r₂=r₁) and that the height doubles (h₂ = 2h₁). If you substitute these values into the equation for the volume of V₂, you get:

 

V₂ = π(r₂)²(h₂) <=>

V₂ = π(r₁)²(2h₁) <=>

V₂ = 2 πr₁²h₁ = 2 V₁