Answer:
The first first box needs 600 [tex]cm^2[/tex] more brown paper for wrapping
Step-by-step explanation:
Given:
First box:
Square base
Length of the base side = 30 cm
Height of the pyramid = 45 cm
Second Box:
octagonal base
base perimeter = 120 cm
width = 10 cm
Height = 35 cm
To Find:
Which box requires more paper to wrap, and by how much?
Solution:
To Find the amount are brown paper needed to wrap, lets find the surface area of the pyramids
Step: Finding the surface area of the box 1
The First box is square pyramid:
= base square area + 4 x area of side triangle
Base square area:
Area of the square = side x side
= 30 x 30
=900 centimetre square
Area of triangle
=[tex]\frac{1}{2} base \times height[/tex]
=>[tex]\frac{1}{2} (30 \times 45)[/tex]
=>[tex]\frac{1350}{2}[/tex]
=>675 centimetre square
Thus the total brown paper needed for wrapping the first box
= 900 + 675
= 1575 centimetre square--------------------------------(1)
Step 2: Finding the surface area of the box 2
The second box is octagonal pyramid:
= base octagonal area + 8 x area of side triangle
Base octagonal area:
Area of the base of the octagon = 8 x area of one triangle
area of one triangle = [tex]\frac{1}{2} base \times height[/tex]
= [tex]\frac{1}{2} 15 \times 10[/tex]
= [tex]\frac{150}{2}[/tex]
=75 centimetre square
Area of the base of the octagon = 8 x 75 = 600 centimetre square
Area of the side triangles
= [tex]\frac{1}{2} base \times height[/tex]
= [tex]\frac{1}{2} (45 \times 15)[/tex]
=[tex]\frac{675}{2}[/tex]
= 337.5 centimetre square
Thus the total surface of the octagonal pyramid is
= 600 +375
=975 centimetres square -------------------------------(2)
On comparing (1) and(2)
1575 -975 = 600
The first box requires 600 [tex]cm^2[/tex] more brown paper for wrapping
