Example problems: Applying surface area formulas for cylinders

📚 Quick Study Guide

• 📐 The total surface area of a cylinder is the sum of the areas of the two circular bases and the lateral surface.
• 📏 The formula for the area of each circular base is: $A = \pi r^2$, where $r$ is the radius.
• 🌀 The lateral surface area of a cylinder is the area of the rectangle that forms the curved surface when unrolled. The formula is: $LSA = 2 \pi r h$, where $h$ is the height of the cylinder.
• 🧮 Therefore, the total surface area (TSA) formula is: $TSA = 2 \pi r^2 + 2 \pi r h$ or $TSA = 2 \pi r (r + h)$.
• 💡 Remember to use consistent units for radius and height!

Practice Quiz

1. What is the total surface area of a cylinder with a radius of 3 cm and a height of 7 cm?
   1. $188.50 \text{ cm}^2$
   2. $207.35 \text{ cm}^2$
   3. $150.80 \text{ cm}^2$
   4. $125.66 \text{ cm}^2$


2. A cylinder has a radius of 5 inches and a height of 10 inches. Calculate its total surface area.
   1. $471.24 \text{ in}^2$
   2. $235.62 \text{ in}^2$
   3. $392.70 \text{ in}^2$
   4. $549.78 \text{ in}^2$


3. If a cylinder has a diameter of 8 meters and a height of 12 meters, what is its total surface area?
   1. $603.19 \text{ m}^2$
   2. $402.12 \text{ m}^2$
   3. $502.65 \text{ m}^2$
   4. $703.72 \text{ m}^2$


4. Find the total surface area of a cylinder with a radius of 2 cm and a height of 5 cm.
   1. $50.27 \text{ cm}^2$
   2. $62.83 \text{ cm}^2$
   3. $87.96 \text{ cm}^2$
   4. $75.40 \text{ cm}^2$


5. What is the height of a cylinder with a radius of 4 cm and a total surface area of $301.59 \text{ cm}^2$?
   1. $6 \text{ cm}$
   2. $7 \text{ cm}$
   3. $8 \text{ cm}$
   4. $9 \text{ cm}$


6. A cylindrical tank has a radius of 6 feet and a height of 9 feet. What is the total surface area?
   1. $565.49 \text{ ft}^2$
   2. $339.29 \text{ ft}^2$
   3. $169.65 \text{ ft}^2$
   4. $282.74 \text{ ft}^2$


7. Calculate the total surface area of a cylinder with a radius of 10 mm and a height of 3 mm.
   1. $816.81 \text{ mm}^2$
   2. $565.49 \text{ mm}^2$
   3. $628.32 \text{ mm}^2$
   4. $408.41 \text{ mm}^2$