This document provides instruction on calculating the surface areas of cylinders, cones, and spheres. It gives the formulas for surface area of each shape and works through examples of calculating surface areas when given the relevant measurements. It concludes with practice problems asking to calculate the surface areas of various cylinders, cones, and spheres using the formulas provided.

1. 4th Quarter

2. PRAYER
Dear God, Thank you for this day.
Bless me, my classmates, our
teacher, our family, our community,
and our country.
Bless our lesson, our work, and our
play.
Keep us safe throughout the day,
Amen.

4. HAVE FUN AS
YOU LEARN
01

5. Find the surface area of the following figures.

6. CYLINDER CONE SPHERE

7. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑜𝑝 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑡𝑡𝑜𝑚 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋
𝑆𝐴 = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑜𝑝 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑡𝑡𝑜𝑚 + 𝑎𝑟𝑒𝑎 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑓𝑎𝑐𝑒
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑓𝑎𝑐𝑒 = 2 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡 𝑥 𝜋
𝑆𝐴 = 𝑟 𝑥 𝑟 𝑥 𝜋 + 𝑟 𝑥 𝑟 𝑥 𝜋 + 2 𝑥 𝑟 𝑥 ℎ 𝑥𝜋
𝑆𝐴 = (2 𝑥 𝑟 𝑥 𝑟 𝑥 𝜋) + (2 𝑥 𝑟 𝑥 ℎ 𝑥 𝜋)

8. The diameter of the bases of a cylinder is 14 in. if the height of the curved
surface is 14 in, what is the surface area of the cylinder.
𝑆𝐴 = (2 𝑥 𝑟 𝑥 𝑟 𝑥 𝜋) + (2 𝑥 𝑟 𝑥 ℎ 𝑥 𝜋)
𝑆𝐴 = (2 𝑥 7 𝑥 7 𝑥 𝜋) + (2 𝑥 7 𝑥 14 𝑥 𝜋)
𝑆𝐴 = (98 𝑥 𝜋) + (196 𝑥 𝜋)
𝑆𝐴 = (307.87) + (615.75)
𝑆𝐴 = 923.62 𝑠𝑞. 𝑖𝑛

9. s
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑏𝑎𝑠𝑒 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋
𝑠 = 𝑠𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡
s
s
h 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋 𝑥 𝑠𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡
𝑆𝐴 = 𝐴𝑟𝑒𝑎 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑏𝑎𝑠𝑒 + 𝐴𝑟𝑒𝑎 𝑐𝑢𝑟𝑣𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒
𝑆𝐴 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋 + 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑠𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 𝑥 𝜋
𝑆𝐴 = 𝑟 𝑥 𝑟 𝑥 𝜋 + (𝑟 𝑥 𝑠 𝑥 𝜋)

10. Find the surface area of the cone.
𝑆𝐴 = 𝑟 𝑥 𝑟 𝑥 𝜋 + (𝑟 𝑥 𝑠 𝑥 𝜋)
𝑆𝐴 = 5 𝑥 5 𝑥 𝜋 + (5 𝑥 13 𝑥 𝜋)
𝑆𝐴 = 25 𝑥 𝜋 + (65 𝑥 𝜋)
𝑆𝐴 = 78.53 + 204.20
𝑆𝐴 = 282.73 𝑠𝑞. 𝑚

11. 𝑆𝐴 = 4 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋
Find the surface area of the sphere with the radius of 5 cm.
𝑆𝐴 = 4 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝑟𝑎𝑑𝑖𝑢𝑠 𝑥 𝜋
𝑆𝐴 = 4 𝑥 5 𝑥 5 𝑥 𝜋
𝑆𝐴 = 100 𝑥 𝜋
𝑆𝐴 = 314.15

12. A. Calculate the surface area of each cylinder.
𝑆𝐴 = (2 𝑥 𝑟 𝑥 𝑟 𝑥 𝜋) + (2 𝑥 𝑟 𝑥 ℎ 𝑥 𝜋)
1. 𝑑 = 6 𝑐𝑚; ℎ = 8 𝑐𝑚
2. 𝑑 = 8 𝑓𝑡; ℎ = 12 𝑓𝑡
3. 𝑟 = 10 𝑦𝑑; ℎ = 4 𝑦𝑑
Surface area
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B. Calculate the surface area of each cone.
𝑆𝐴 = (𝑟 𝑥 𝑟 𝑥 𝜋) + (𝑟 𝑥 𝑠 𝑥 𝜋)
1. 𝑟 = 4 𝑓𝑡; 𝑠 = 10 𝑓𝑡
2. 𝑑 = 12 𝑖𝑛; 𝑠 = 8 𝑖𝑛
3. 𝑟 = 8.4 𝑦𝑑; 𝑠 = 6 𝑦𝑑
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13. C. Calculate the surface area of each sphere
𝑆𝐴 = 4 𝑥 𝑟 𝑥 𝑟 𝑥 𝜋
1. 𝑟 = 14 𝑚𝑚
2. 𝑑 = 35 𝑚
3. 𝑟 = 3.6 𝑐𝑚
4. 𝑑 = 4.6 𝑚
5. 𝑟 = 6. 𝑚
Surface area
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14. “More Practice”
Pages 363-364
ACTIVITY A & B

15. Thanks!