Question

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm. The volume of the liquid in the first graduated cylinder is 188.4 cm3. The volume of the liquid in the second graduated cylinder is 314 cm3.

What is the difference in the height of the liquid in the two cylinders?

Use 3.14 to approximate pi.

Answer 1

Volume of a cylinder of radius r, height h :
`V=\pi*r^2*h`

hence the height of the liquid in the first cylinder is
`h1=(188.4)/(2^2\pi)=15` cm, and in the second cylinder
`h2=(314)/(2^2\pi)=25` cm

Hence the difference is h2-h1=25-15=10 cm

Answer 2

The difference of height is 10 cm

Explanation:

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm.

The volume of the liquid in the first graduated cylinder is 188.4 cm³

The volume of the liquid in the second graduated cylinder is 314 cm³

Let height of first graduated cylinder be h₁ and radius (r) = 2 cm

Let height of second graduated cylinder be h₂ and radius (r) = 2 cm

Formula:

`\text{Volume of cylinder}=\pi r^2h`

`\text{Volume of 1st cylinder}=\pi\cdot 2^2h_1`

`188.4=3.14\cdot 2^2\cdot h_1`

`h_1=15` cm

`\text{Volume of 2nd cylinder}=\pi\cdot 2^2h_2`

`314=3.14\cdot 2^2\cdot h_2`

`h_2=25` cm

The difference in the height of the liquid in two cylinder,

`\Rightarrow h_2-h_1`

`\Rightarrow 25-15`

`\Rightarrow 10` cm

Hence, The difference of height is 10 cm