Lesson Plans SET B for Grades 9-10-Lesson 10 Level 9-10 3D Geometry

Lesson 10 Level 9-10 3D Geometry - HW

Pdf Summary

The document contains a set of exercises on 3D Geometry designed for Level 9-10 students preparing for Math Kangaroo competitions. There are five main problems highlighted:<br /><br />1. **Volume and Surface Area Relationship**: Students are required to find relationships between the surface areas of a sphere, a cube, and an equilateral cylinder, given their equal volumes. The correct answer is option B, where \( S_2 > S_3 > S_1 \).<br /><br />2. **Rhombus Folding and Distance Calculation**: This problem involves forming a dihedral angle by folding a rhombus with side length 1 and angles of 60 degrees. Students must calculate the minimum and maximum distance between two diagonals, which are \( \frac{\sqrt{3}}{4} \) and \( \frac{3\sqrt{3}}{4} \), respectively.<br /><br />3. **Swimming Pool Volume**: The task is to compute the volume of water in an in-ground swimming pool using given dimensions, resulting in a volume calculation of \( 534 \, m^3 \).<br /><br />4. **Empty Space in a Tennis Ball Tube**: Students need to compute the proportion of empty space when three tennis balls (diameter of 2.7 inches each) are packed in a cylindrical tube. The empty space proportion is calculated as \( \frac{1}{3} \).<br /><br />5. **Additional Empty Space Calculations**: Using the geometry from the previous problem, students must determine the empty space proportions for tubes containing four and five tennis balls, respectively, with both sharing the same proportion of \( \frac{1}{3} \).<br /><br />The document offers detailed solutions and logical processes to guide students through each problem, using geometric principles and algebraic equations to arrive at the correct answers. These tasks provide practice in linking theory to practical applications in geometry, requiring proficiency in volume, surface area calculations, and understanding spatial relationships.

Keywords

3D Geometry

Math Kangaroo

Volume Surface Area

Sphere Cube Cylinder

Rhombus Folding

Dihedral Angle

Swimming Pool Volume

Tennis Ball Tube

Empty Space Calculation

Geometric Principles