6. The diameter of a circular microorganism is 8.8 nanometres. Find the (i) circumference in m , (ii) area in $$ \mathrm{m}^{2} $$, of the microorganism. Give your answers in standard form. (Take $$ \pi=3.142,1 $$ nanometre $$ =10^{-9} $$ metres.)

Question

UpStudy AI · Accepted Answer

Let the diameter be given by  
$$
d = 8.8 \times 10^{-9} \text{ m}.
$$

### (i) Circumference

The formula for the circumference is  
$$
C = \pi d.
$$

Substitute the given values:  
$$
C = 3.142 \times \left(8.8 \times 10^{-9}\right).
$$

Calculate the product:  
$$
3.142 \times 8.8 = 27.6496.
$$

Thus,  
$$
C = 27.6496 \times 10^{-9} \text{ m}.
$$

To express in standard form, we write:  
$$
27.6496 \times 10^{-9} = 2.76496 \times 10^{-8} \text{ m}.
$$

Rounded to three significant figures,  
$$
C \approx 2.76 \times 10^{-8} \text{ m}.
$$

### (ii) Area

The area $$A$$ of a circle is given by:  
$$
A = \pi r^2,
$$
where the radius $$r$$ is half the diameter. Thus,  
$$
r = \frac{d}{2} = \frac{8.8 \times 10^{-9}}{2} = 4.4 \times 10^{-9} \text{ m}.
$$

Now calculate the area:  
$$
A = 3.142 \times \left(4.4 \times 10^{-9}\right)^2.
$$

First, compute the square of the radius:  
$$
\left(4.4 \times 10^{-9}\right)^2 = 4.4^2 \times \left(10^{-9}\right)^2 = 19.36 \times 10^{-18}.
$$

Then,  
$$
A = 3.142 \times 19.36 \times 10^{-18}.
$$

Calculate the product:  
$$
3.142 \times 19.36 = 60.851712.
$$

Thus,  
$$
A = 60.851712 \times 10^{-18} \text{ m}^2.
$$

Express in standard form:  
$$
60.851712 \times 10^{-18} = 6.0851712 \times 10^{-17} \text{ m}^2.
$$

Rounded to three significant figures,  
$$
A \approx 6.09 \times 10^{-17} \text{ m}^2.
$$

### Final Answers

$$
\text{(i) } C \approx 2.76 \times 10^{-8} \text{ m} \quad \text{and} \quad \text{(ii) } A \approx 6.09 \times 10^{-17} \text{ m}^2.
$$
The diameter of the microorganism is 8.8 nanometres. (i) The circumference is approximately $$ 2.76 \times 10^{-8} $$ metres. (ii) The area is approximately $$ 6.09 \times 10^{-17} $$ square metres.

The diameter of a circular microorganism is
8.8 nanometres. Find the
(i) circumference in m ,
(ii) area in ,
of the microorganism.
Give your answers in standard form.
(Take nanometre metres.)

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(i) Circumference

(ii) Area

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The diameter of a circular microorganism is 8.8 nanometres. Find the (i) circumference in m , (ii) area in , of the microorganism. Give your answers in standard form. (Take nanometre metres.)