Question

Soup can be packaged in two different containers: a box and a cylinder. The dimensions of the box are 7.5 cm by 4.7 cm by 14.5 cm. The cylinder has a radius of 3.3 cm and a height of 10 cm. Determine which container uses less material to make and find out which container holds more soup.

Answer 1

Answer: Cylinder uses less material to make.

Box holds more soup then cylinder.

Explanation:

Total surface area of cuboidal box =2(lw+wh+lh), l= length, w=width, h=height

Total surface area of cylinder =
`2\pi r(r+h)` 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 =
`2(3.14)(3.3)(3.3+10)`
`=275.63\ \text{ sq. cm}`

[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 =
`\pi r^2h`

`=(3.14)(3.3)^2(10)`

= 341.946 cubic cm

As (Volume of box) > (Volume of cylinder )

So, Box holds more soup then cylinder.