Answer: Cylinder uses less material to make.
Box holds more soup then cylinder.
Step-by-step explanation:
Total surface area of cuboidal box =2(lw+wh+lh), l= length, w=width, h=height
Total surface area of cylinder = [tex]2\pi r(r+h)[/tex] where r= radius and h is height.
Given , Dimension of box : 7.5 cm by 4.7 cm by 14.5 cm
Dimension of cylinder : radius of 3.3 cm and a height of 10 cm.
Total surface area of box =2((7.5)(4.7)+(4.7)(14.5)+(7.5)(147.5)) sq. cm
= 2(1209.65)
=2419.3 sq. cm
Total surface area of cylinder = [tex]2(3.14)(3.3)(3.3+10)[/tex][tex]=275.63\ \text{ sq. cm}[/tex]
[π=3.14]
(Total surface area of cylinder)<(Total surface area of box )
So, cylinder uses less material to make.
Volume of box = l x w x h
= (7.5)(4.7)(14.5) = 511.13 cubic cm
Volume of cylinder = [tex]\pi r^2h[/tex]
[tex]=(3.14)(3.3)^2(10)[/tex]
= 341.946 cubic cm
As (Volume of box) > (Volume of cylinder )
So, Box holds more soup then cylinder.
