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Please help!!!

A shipping company sells two different types of cardboard boxes shaped as regular pyramids. The first box has a square base with side length 30 cm and height 45 cm. The second box has an octagonal base with a perimeter of 120 cm and a distance of 10 cm from the centre of the base to the midpoint of each side. The second box has a height of 35 cm. Each box needs to be wrapped in brown paper for shipping. Which box requires more paper, and by how much? Express your answer in cm^2

Respuesta :

carlosego
The answer is: The first box.
 The explanation is shown below:
 1. You must apply the formula for calculate the area of regular pyramid, which is:
 A=Base area+(PerimeterxSlant height)/2
 2. The area of the first box is:
 Slant heigth=√(45 cm)²+(15 cm)²
 Slant height=47.43
 A1=(30 cm)²+(30 cmx4)(47.43 cm)/2
 A1=3745.8 cm²
 2. The area of the second box is:
 Slant heigth=√(35 cm)²+(10 cm)²
 Slant height=36.40 cm
 Base area=(10 cmx7.5 cm/2)16
 Base area=600 cm²
 A2=600 cm²+(120 cm)(36.40 cm)/2
 A2=2784 cm²
 3. Therefore A1>A2

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