Question

An open

circular patch of liquid in an industrial process has a density 0.8 g/cm³. The
diameter of the patch is 0.2 m and the thickness is 3 mm. Assuming that the patch of
liquid is in the shape of a cylinder, find the mass of the liquid.

Answer 1

75.4 grams

Explanation:

To find the mass of the liquid, we can use the following formula:

`\boxed{\boxed{\sf Mass = Density * Volume}}`

The density of the liquid is 0.8 g/cm³, the diameter of the patch is 0.2 m, and the thickness is 3 mm.

We need to convert the diameter and thickness to cm before we can calculate the volume.

Diameter = 0.2 m × 100 cm/m = 20 cm

Thickness = 3 mm × 1 cm/10 mm = 0.3 cm

The radius of the patch is half the diameter, or 10 cm.

We have

`\boxed{\boxed{\textsf{ Volume of cylinder } = \sf \pi * radius^2 * height}}`

Substitute the known value and simplify:

`\begin{aligned} \textsf{ Volume of cylinder } & = \sf \pi * 10^2 * 0.3 \\\\ & = 30 \pi \textsf{ cm}^2 \end{aligned}`

Now we can calculate the mass of the liquid:

Mass = 0.8 g/cm³ × 30π cm^3

Mass = 24π g

Mass = 75.398223686155 g

Mass ≈ 75.4g ( in 1 d.p.)

Therefore, the mass of the liquid is 75.4 grams.

Answer 2

75.4 g

Explanation:

To find the mass of the liquid, we first need to find its volume by using the formula for the volume of a cylinder:

`V = \pi r^2 h`

where:

• r is the radius of the cylinder.
• h is the height.

The radius of circle is half its diameter. Therefore, the radius is:

`r = \frac{0.2 \; \text{m}}{2} = 0.1 \; \text{m}`

Convert this to centimeters:

`r = 0.1 \; \text{m}* \frac{100 \; \text{cm}}{1 \; \text{m}}=10\; \text{cm}`

Convert the height (thickness) to centimeters for consistent units:

`h = 3 \; \text{mm} * \frac{1 \; \text{cm}}{10 \; \text{mm}} = 0.3 \; \text{cm}`

Substitute these values into the formula for the volume:

`V = \pi * (10 \; \text{cm})^2 * 0.3 \; \text{cm}`

`V=30\pi\; \text{cm}^3`

Now, multiply the volume by the given density of 0.8 g/cm³ to find the mass:

`\text{Mass} = \text{Density} * \text{Volume}`

`\text{Mass} = \frac{0.8 \; \text{g}}{\text{cm}^3} * 30\pi\;\text{cm}^3`

`\text{Mass} = 24\pi\;\text{g}`

`\text{Mass} =75.398223686...\;\text{g}`

`\text{Mass} =75.4\;\text{g}\; \text{(nearest\;tenth)}`

Therefore, the mass of the liquid is 75.4 g (rounded to the nearest tenth).