Circles, Angles, and 3D Geometry
Grade 7 Mathematics Exploring geometric relationships and real-world applications
Think About It
If you wanted to measure the area of a pizza or figure out how much wrapping paper you need to cover a cylindrical can, what measurements would help?
Key Vocabulary Review
Radius: Distance from center to edge of circle Diameter: Distance across circle through center Circumference: Distance around the circle Central angle: Angle formed at the center of a circle Surface area: Total area of all faces of a 3D shape Volume: Amount of space inside a 3D shape
Angles in Circles
Central angles are formed at the center of a circle Complementary angles add up to 90° Supplementary angles add up to 180° Vertical angles are equal when lines intersect Example: If a central angle is 70°, its supplement is 110°
Circle Area Challenge
Formula: A = πr² Remember: Use radius, not diameter! Practice: Calculate the area of a pizza with radius 6 inches Extension: Find the area of a 60° slice of the same pizza
Surface Area and Volume Formulas
{"left":"Surface Area of Cylinder: 2πr² + 2πrh\nVolume of Cylinder: πr²h\nSurface Area of Prism: 2(lw + lh + wh)","right":"Volume of Prism: Base Area × Height\nAlways include units in your answer!\nRound to appropriate decimal places"}
Real-World Problem Solving
Water Tank: A cylindrical tank has radius 4 ft and height 7 ft. Find its volume. Box Painting: A rectangular box measures 3 ft × 2 ft × 1 ft. Find the surface area to paint. Work in pairs to solve these problems Show all work and include units!
Exit Ticket Challenge
Calculate the volume of a cylinder with radius 3 m and height 5 m What is the supplementary angle if one angle measures 120°? Write your answers on your mini whiteboard