Let's solve each cylinder's
total surface area step by step.
The
formula for the total surface area (SA) of a cylinder is:
$$
\text{SA} = 2\pi r^2 + 2\pi r h
$$
Where:
- $ r $ = radius
- $ h $ = height
- $ \pi \approx 3.14 $
We will use this formula for all cylinders, rounding final answers to the
nearest whole number.
---
1.
- Diameter = 8 in → Radius $ r = \frac{8}{2} = 4 $ in
- Height $ h = 2 $ in
$$
\text{SA} = 2(3.14)(4)^2 + 2(3.14)(4)(2)
= 2(3.14)(16) + 2(3.14)(8)
= 100.48 + 50.24 = 150.72
$$
Rounded:
151
---
2.
- Radius $ r = 3.5 $ in
- Height $ h = 5 $ in
$$
\text{SA} = 2(3.14)(3.5)^2 + 2(3.14)(3.5)(5)
= 2(3.14)(12.25) + 2(3.14)(17.5)
= 76.93 + 109.9 = 186.83
$$
Rounded:
187
---
3.
- Diameter = 4 in → Radius $ r = 2 $ in
- Height $ h = 2.25 $ in
$$
\text{SA} = 2(3.14)(2)^2 + 2(3.14)(2)(2.25)
= 2(3.14)(4) + 2(3.14)(4.5)
= 25.12 + 28.26 = 53.38
$$
Rounded:
53
---
4.
- Diameter = 9 in → Radius $ r = 4.5 $ in
- Height $ h = 12 $ in
$$
\text{SA} = 2(3.14)(4.5)^2 + 2(3.14)(4.5)(12)
= 2(3.14)(20.25) + 2(3.14)(54)
= 127.17 + 339.12 = 466.29
$$
Rounded:
466
---
5.
- Diameter = 6 in → Radius $ r = 3 $ in
- Height $ h = 13 $ in
$$
\text{SA} = 2(3.14)(3)^2 + 2(3.14)(3)(13)
= 2(3.14)(9) + 2(3.14)(39)
= 56.52 + 244.92 = 301.44
$$
Rounded:
301
---
6.
- Diameter = 2 in → Radius $ r = 1 $ in
- Height $ h = 2 $ in (from the side)
$$
\text{SA} = 2(3.14)(1)^2 + 2(3.14)(1)(2)
= 2(3.14)(1) + 2(3.14)(2)
= 6.28 + 12.56 = 18.84
$$
Rounded:
19
---
✔ Final Answers:
| Figure | Work Area | Answer |
|-------|-----------|--------|
| 1 | $ 2(3.14)(4)^2 + 2(3.14)(4)(2) = 150.72 $ |
151 |
| 2 | $ 2(3.14)(3.5)^2 + 2(3.14)(3.5)(5) = 186.83 $ |
187 |
| 3 | $ 2(3.14)(2)^2 + 2(3.14)(2)(2.25) = 53.38 $ |
53 |
| 4 | $ 2(3.14)(4.5)^2 + 2(3.14)(4.5)(12) = 466.29 $ |
466 |
| 5 | $ 2(3.14)(3)^2 + 2(3.14)(3)(13) = 301.44 $ |
301 |
| 6 | $ 2(3.14)(1)^2 + 2(3.14)(1)(2) = 18.84 $ |
19 |
>
✔ All answers are rounded to the nearest whole number.
Let me know if you'd like this formatted as a printable table!
Parent Tip: Review the logic above to help your child master the concept of surface area cylinder worksheet.
