Question

The volume of a cylinder increased by 8 times the original volume. How many times greater are each of the dimensions of that new cylinder?

2

3

4

8

Answer 1

they are only double... the reasoning... is that the linear measurements are cubed to get volume...

test it with a cylinder radius 1 unit height 1 unit...

find the volume

then cylinder, radius 2 units and height 2 units

then compare them

Answer 2

@campbell_st , I got C)

Answer 3

well C is wrong...

radius = 1 height = 1

\[V = \pi \times1^1 \times 1 = \pi\]

radius = 2 and height = 2

\[V = \pi \times 2^2 \times 2 = 8\pi... \]

if you triple the measurements the volume increased by 3^3 or 27

so

r = 3 and h = 3

\[V = \pi \times 3^2 \times 3 = 27\pi\]

quadruple the measurements the increase is 4^3 or 64 times

hopefully it helps you to understand the concept

Answer 4

so is the volume has increase by 8 times

take the cube root...

\[\sqrt[3]{8} = 2\]

so the linear measurements were doubled