Question

Okay so, this is my friends work, I completely failed 8th and am trying to relearn and help lol, I know Pie times 25 equals 78.5, is the area of one circle, and twice that is 2 circles, I dont even know if thats wrong or right and my dad will yell at me if I even have 1 digit off, so Im completely hopeless and am desperate for help. (Added Photo)

Answer 1

1. a) rectangle, circles.

1. b) circumference.

2. half.

3. 2πr² + 2πrh

4. See below.

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

`\textsf{Circumference of a circle} = \pi d=2 \pi r`

Therefore, the formula for the surface area of a cylinder is:

`\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}`

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:

• 2r × π × h

Question 4a

Given:

• Radius = 5 cm
• Height = 6 cm

Area of One Circle

`\begin{aligned} \pi * r^2&=3 * (5)^2\\&=3 * 25\\&=75\; \sf cm^2\end{aligned}`

Area of Two Circles

`75 * 2 = 150\; \sf cm^2`

Area of Rectangle

`\begin{aligned}2r * \pi * h&=2(5) * 3 * 6\\&=10 * 3* 6\\&=30 * 6\\&=180\; \sf cm^2\end{aligned}`

Total Surface Area

`\;\;\;\;180+150\\=330\sf \; cm^2`

Question 4b

Given:

• Radius = 6.2 cm ≈ 6 cm
• Height = 12.3 cm ≈ 12 cm

Area of One Circle

`\begin{aligned} \pi * r^2&=3 * (6)^2\\&=3 * 36\\&=108\; \sf cm^2\end{aligned}`

Area of Two Circles

`108 * 2 = 216\; \sf cm^2`

Area of Rectangle

`\begin{aligned}2r * \pi * h&=2(6) * 3 * 12\\&=12 * 3* 12\\&=36 * 12\\&=432\; \sf cm^2\end{aligned}`

Total Surface Area

`\;\;\;\;432+216\\=648 \sf \;cm^2`

Question 4c

Given:

• Radius = 10.7 cm ≈ 11 cm
• Height = 17.4 cm ≈ 17 cm

Area of One Circle

`\begin{aligned} \pi * r^2&=3 * (11)^2\\&=3 * 121\\&=363\; \sf cm^2\end{aligned}`

Area of Two Circles

`363* 2 = 726\; \sf cm^2`

Area of Rectangle

`\begin{aligned}2r * \pi * h&=2(11) * 3* 17\\&=22 * 3 * 17\\&=66 * 17\\&=1122\; \sf cm^2\end{aligned}`

Total Surface Area

`\;\;\;\;1122+726\\=1848\sf \;cm^2`