Answer:
1. a) rectangle, circles.
1. b) circumference.
2. half.
3. 2πr² + 2πrh
4. See below.
Step-by-step explanation:
Question 1
a) The net of a cylinder is made up of one rectangle and two circles.
b) The width of the rectangle in the net of a cylinder is equal to the circumference of the circle.
Question 2
The radius of a circle is half the diameter.
Question 3
[tex]\textsf{Circumference of a circle} = \pi d=2 \pi r[/tex]
Therefore, the formula for the surface area of a cylinder is:
[tex]\begin{aligned}\textsf{S.A. of a cylinder}&=\sf 2\;circles+1\;rectangle\\&=2 \pi r^2+2\pi rh\\&=2\pi r(r+h)\end{aligned}[/tex]
where r is the radius of the circle and h is the height of the cylinder.
Note: It appears from the question sheet that they wish you to use π=3.
Also, as you need to estimate the total surface area, round any decimals to their nearest whole number before carrying out any calculations.
Please note that the formula for Area of Rectangle quoted in the example question is incorrect when comparing it to the answer of question 1b. In the formula, it says that the length is equal to the circumference of the circle, whereas in question 1b it states that the width of the rectangle is equal to the circumference. Therefore, I have used the correct formula for the rectangle part of the cylinder:
Question 4a
Given:
- Radius = 5 cm
- Height = 6 cm
Area of One Circle
[tex]\begin{aligned} \pi \times r^2&=3 \times (5)^2\\&=3 \times 25\\&=75\; \sf cm^2\end{aligned}[/tex]
Area of Two Circles
[tex]75 \times 2 = 150\; \sf cm^2[/tex]
Area of Rectangle
[tex]\begin{aligned}2r \times \pi \times h&=2(5) \times 3 \times 6\\&=10 \times 3\times 6\\&=30 \times 6\\&=180\; \sf cm^2\end{aligned}[/tex]
Total Surface Area
[tex]\;\;\;\;180+150\\=330\sf \; cm^2[/tex]
Question 4b
Given:
- Radius = 6.2 cm ≈ 6 cm
- Height = 12.3 cm ≈ 12 cm
Area of One Circle
[tex]\begin{aligned} \pi \times r^2&=3 \times (6)^2\\&=3 \times 36\\&=108\; \sf cm^2\end{aligned}[/tex]
Area of Two Circles
[tex]108 \times 2 = 216\; \sf cm^2[/tex]
Area of Rectangle
[tex]\begin{aligned}2r \times \pi \times h&=2(6) \times 3 \times 12\\&=12 \times 3\times 12\\&=36 \times 12\\&=432\; \sf cm^2\end{aligned}[/tex]
Total Surface Area
[tex]\;\;\;\;432+216\\=648 \sf \;cm^2[/tex]
Question 4c
Given:
- Radius = 10.7 cm ≈ 11 cm
- Height = 17.4 cm ≈ 17 cm
Area of One Circle
[tex]\begin{aligned} \pi \times r^2&=3 \times (11)^2\\&=3 \times 121\\&=363\; \sf cm^2\end{aligned}[/tex]
Area of Two Circles
[tex]363\times 2 = 726\; \sf cm^2[/tex]
Area of Rectangle
[tex]\begin{aligned}2r \times \pi \times h&=2(11) \times 3\times 17\\&=22 \times 3 \times 17\\&=66 \times 17\\&=1122\; \sf cm^2\end{aligned}[/tex]
Total Surface Area
[tex]\;\;\;\;1122+726\\=1848\sf \;cm^2[/tex]
