Pi Day Covering flower pot
- 1. PI DAY Covering a flower pot We measured the circumference and height of a few pots of flowers in our school. We want to cover the lateral surface of the pot with a decorative paper. What surface should have the decorative paper for this action? We obtained the circumference of the great circle 𝑳 𝟏 = 𝟏𝟐𝟔 𝒄𝒎 We obtained the circumference of the little circle 𝑳 𝟐 = 𝟔𝟑 𝒄𝒎 Height of the pot is h=40 cm 𝑳 𝟏 = 𝟐𝝅𝑹 ⟹ 6,28 ⋅ 𝑅 = 126 ⟹ 𝑅 ≃ 20,06 ≈ 20 ⟹ ⟹ 𝑹 ≈ 𝟐𝟎 𝒄𝒎 𝑳 𝟐 = 𝟐𝝅𝒓 ⟹ 6,28 ⋅ 𝑟 = 63 ⟹ 𝑅 ≃ 10,03 ≈ 10 ⟹ ⟹ 𝒓 ≈ 𝟏𝟎 𝒄𝒎 𝐶𝐸 ⊥ 𝐴𝐵 ⟹ 𝐺2 = ℎ2 + (𝑅 − 𝑟)2 ⟹ ⟹ 𝐺2 = 1600 + 100 ⟹ ⟹ 𝑮 = 𝟒𝟏, 𝟐 cm ⟹ 𝑨𝒍 = 𝝅𝑮(𝑹 + 𝒓) ⟹ 𝑨𝒍 = 𝟑, 𝟏𝟒 ⋅ 𝟒𝟏, 𝟐(𝟐𝟎 + 𝟏𝟎) 𝑨𝒍 = 𝟑𝟖𝟖𝟏 𝒄𝒎 𝟐
- 2. The radius of the cone which result from the truncated con is R=10. Lateral surface of the cone in which the trunk of cone is a circular sector with radius as the cone generator R. We must calculate the measure of the angle of the cicular sector 𝑚(∡𝐴𝑉𝐴") = 𝑛° . Lateral surface of the truncated cone is a circular crown. The areaof the circular crown is 3881. 𝑉𝐴 𝑉𝐶 = 𝑟 𝑅 = 1 2 ⟹ 𝑉𝐴 = 𝐴𝐶 = 41,2 ⟹ 𝐶𝑉 = 82,4 ⟹ The length of circular arc is 𝐿 = 𝜋𝑅𝑛∘ 180∘ , where R=CV ⟹ 𝜋∙82,4∙𝑛∘ 180∘ = 126 ⟹ 𝑛° = 126∙180° 82,4𝜋 ⟹ 𝑛° ≈ 88° . Considering the joints, we need 𝑛° ≈ 90° . The area of MCVC’ is the area of a square. A=l2 =6790 cm2 =0,679m2 . So we need 0,7 m2 paper for our pot. Andra Pitiș, Ann Miess Chisthine – clasa a VIII-a B