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Name:_____________________________________________________ Date:_____________________ Geometric Fashion Week Unit 6 Integrated Math II _____________________________________________________________________________________ 1. Explain why increasing the radius by a constant increases the volume of a cylinder more than increasing the height by the same constant. Use examples and complete sentences. You will not get full credit unless you write AT LEAST THREE SENTENCES. 2. How can you derive the area of a circle using the formula of the circumference of a circle? 3. Find the perimeter and the area of the following: 4. There is a park with a radius of 200 m. The park has 3 benches that are 1 m wide and 2.5 m long. The park also has 8 lamps where the bases are 1m in diameter. Find the area of the park which excludes the benches and the lamps. 5. Using the figure above, find the area of the border around the black triangle. Both triangles are equilateral. 6. Find the volume for the following figure: 7. After a maximum number of 3-cm plastic cubes are packed into a rectangular box measuring 32 cm by 22 cm by 13 cm, what is the volume of the space left in the box? 8. Find “x” in the following figure given that the volume is equal to 165 cm cubed. 9. Find the surface area of the following figure: 10. A cubical container was completely filled with oil. All the oil was then poured into a larger rectangular container, 128cm by 32 cm by 4 cm, filling 25% of it. What is the length of the cubical container?