Question

4. The diameter of a circular microorganism is 8.8 nanometres. Find the (i) circumference in m, (ii) area in m², of the microorganism. Give your answers in standard form. (Take π = 3.142, 1 nanometre = 10-9 metres.)

Answer 1

Convert first the given diameter from nanometers to meter.

`8.8\text{ nm}\rightarrow8.8*10^(-9)\text{ m}`

Now that we have the diameter. Find the radius to be able to solve for its circumference and area.

`\begin{gathered} r=\frac{8.8*10^(-9)\text{ m}}{2} \\ r=4.4*10^(-9)\text{ m} \end{gathered}`

Part I: Finding the circumference.

`\begin{gathered} C=2\pi r \\ C=2(3.142)(4.4*10^(-9)\text{ m}) \\ C=2.76496*10^(-8)\text{ m} \end{gathered}`

In standard form, the circumference of the microoraganism is 2.76496 × 10⁻⁸ m.

Part II: Finding the area

`\begin{gathered} A=\pi r^2 \\ A=(3.142)(4.4*10^(-9)\text{ m})^2 \\ A=6.082912*10^(-17)\text{ m}^2 \end{gathered}`

In standard form, the area of the microorganism is 6.082912 × 10⁻¹⁷ m²