Question

Hello everyone! Can you please help me with this problem, and when available, will give out brainliest! Thnx!

Answer 1

Answer:

The first first box needs  600 $cm^2$ 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

=$\frac{1}{2} base \times height$

=>$\frac{1}{2} (30 \times 45)$

=>$\frac{1350}{2}$

=>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 =  $\frac{1}{2} base \times height$

= $\frac{1}{2} 15 \times 10$

= $\frac{150}{2}$

=75 centimetre square

Area of the base of the octagon = 8 x 75 = 600 centimetre square

Area of the side triangles  

=   $\frac{1}{2} base \times height$

= $\frac{1}{2} (45 \times 15)$

=$\frac{675}{2}$

= 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 $cm^2$ more brown paper for wrapping