1) The document describes measuring the circumference and height of flower pots to determine how much decorative paper is needed to cover the lateral surface. 2) It calculates the circumferences and radii of the top and bottom circles of the pot, as well as the height and slanted distance between them. 3) Based on the calculated surface area of the truncated cone shape of the pot, it determines that 0.7 square meters of decorative paper is needed to fully cover the lateral surface.

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