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 𝑳𝟏 = 𝟏𝟐𝟔 𝒄𝒎

We obtained the circumference of the little circle 𝑳𝟐 = 𝟔𝟑 𝒄𝒎

Height of the pot is h=40 cm

𝑳𝟏 = 𝟐𝝅𝑹 ⟹ 6,28 ⋅ 𝑅 = 126

⟹ 𝑅 ≃ 20,06 ≈ 20 ⟹

⟹ 𝑹 ≈ 𝟐𝟎 𝒄𝒎

𝑳𝟐 = 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 𝒄𝒎𝟐

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 cm

2=0,679m

2.

So we need 0,7 m2 paper for our pot.

Andra Pitiș, Ann Miess Chisthine – clasa a VIII-a B