How many times larger is the new volume of a cylinder if the radius is doubled and the height remains the same?

Question

please help

Answer 1

V = (pi)r²h is the formula for the volume of a cylinder.

 

The formula becomes V = (pi)(2r)²h if the radius is doubled and the height remains the same.

V = 4(pi)r²h after simplifying. 

 

The volume increases 4 times since the resulting equation is 4 times the original equation.

 

I'm available for online tutoring if needed.

Answer 2

Hi,

This problem does not involve as much math as you may think. Call the volume of the original cylinder V₁ and the volume of the new cylinder V_2. The generic volume equation for a cylinder is given as V = πr² h where π or pi, is a constant, r is the radius of the top or bottom of the cylinder and h is the height of the cylinder. So comparing V₂ to V₁ gives you a constant, k, or the increase in size of V₂ compared to V₁.  V₂/V₁ = k = π(2r)² h/ π(r)² h.  π, r² and h are the same values for each cylinder so they cancel each other out and that leaves you with k = 2²/1 or k = 4. The new cylinder will have a volume that is 4 times larger than the original cylinder.

Answer 3

The formula for the volume of a cylinder is V = πr²h  (that first symbol is "pi" in case you can't tell, it sort of looks like an "n" to me...).  So r is some value, and then we double it, what happens to the volume?  Let's say original r = x, and doubled r = 2x.

 

Original volume = π(x)²h = πhx²

 

The new volume after doubling r would be π(2x)²h = 4πhx²

 

Therefore the new volume would be 4 times the original volume.  Hope that helps!  :)

Answer 4

Four (4). Since volume varies as the third power, any shape where the volume is dependent on a single variable such as a cube (side^3) or a sphere (r^3), it would simply be the new dimensional size^3 but, since the volume of a cylinder (pi*r^2*h) varies as the square of the radius and the height, but the height is constrained in this case, it would be the new radius^2 = 2^2 = 4.