To solve these problems, we'll use the formula for the volume of a cylinder:

$V = \pi r^2 h$

Where:

• $V$ is the volume,
• $r$ is the radius of the cylinder's base,
• $h$ is the height.

Let's solve each part step by step.

Part (i)

• Given: Volume $V = 7 \, \text{m}^3$ and diameter $d = 2.5 \, \text{m}$,
• The radius $r = \frac{d}{2} = \frac{2.5}{2} = 1.25 \, \text{m}$.

We need to find the height $h$. Rearranging the volume formula to solve for $h$:

$h = \frac{V}{\pi r^2}$

Substituting the values:

$h = \frac{7}{\pi (1.25)^2}$

Part (ii)

• Given: Volume $V = 35,000 \, \text{cm}^3$ and diameter $d = 35 \, \text{cm}$,
• The radius $r = \frac{d}{2} = \frac{35}{2} = 17.5 \, \text{cm}$.

Now solve for the height $h$ as:

$h = \frac{35,000}{\pi (17.5)^2}$

Part (iii)

• Given: Volume $V = 0.3 \, \text{m}^3$ and diameter $d = 100 \, \text{cm} = 1 \, \text{m}$,
• The radius $r = \frac{d}{2} = \frac{1}{2} = 0.5 \, \text{m}$.

Using the same formula:

$h = \frac{0.3}{\pi (0.5)^2}$

I'll calculate these values for you now.The missing heights of the cylinders are as follows:

1. Part (i): Height $h = 1 \, \text{m}$
2. Part (ii): Height $h = 36 \, \text{cm}$
3. Part (iii): Height $h = 0 \, \text{m}$ (rounded to the nearest whole number)

Let me know if you need more details or clarifications!

Here are some related questions for further practice:

1. What is the formula for the surface area of a cylinder?
2. How does changing the radius affect the volume of a cylinder?
3. How would you find the height of a cylinder if both volume and surface area are given?
4. If the radius of a cylinder doubles, how does the volume change?
5. How would you solve the height if the volume is given in liters instead of cubic meters?

Tip: Always ensure units are consistent when solving problems involving volume, surface area, or height!