OUR LADY OF MERCY SCHOOL

Name: Andrei M., Fernanda R., Leonardo W., and Marcelo Vieira        Grade: 9th

Teacher: Ms. Freire & Ms. Oliveira                   Date: Monday, June 11^th, 2001

ARCOS DA LAPA is an engineering and architectural construction work that symbolizes Rio de Janeiro’s colonial period. It was inaugurated, as reported, in 1750, under the government of Ayres de Saldanha and administered by the engineer José Fernandes Alpoim. It was built in order to end the problem of the constant lack of water in Rio de Janeiro towards the end of the XVIII century. The aqueduct would then take the water to the fountain constructed in the Largo da Carioca, and thus distribute it to the population. The Aqueduct of Carioca, as it is also known, was built in Roman style with granite, cement made of limestone, sand, bricks, and whale oil. Extending between the hills of Santa Teresa and Santo Antônio, it is 270 meters long and approximately 18 meters high, presenting two lines of rows, one on top of the other, making a total of 42 perfect arches in each row. It has been in use since 1896 as a viaduct for the trolleys that go from Largo da Carioca to Santa Teresa. It is the district’s most important means of collective transportation and the only system of trolleys that still exists in Rio. It received historical registration by SPHAN (National Secretary of Historical and Artistic Patrimony), and entered the fine arts’ book.

MATH PROBLEM

a)     What is the area of each arch?

b)       What is the total area of the arches located on the upper part?

SOLUTION

a)     Area of Rectangle + Area of semicircle = Area of each arch

Area of rectangle = (8 x 2) m² = 16 m²

Area of Semicircle = ½ (radius)² π  = ½ 1² π = 0.5 π m²

Area of Arch = 16m² + 0.5 π m² = (16 + 0.5 π) m² (or ≈ 17.57 m²)

b)    Total area of arches on the upper part = 1 arch’s total area x 42

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