Question

A can of tomato soup is 4-inches tall and has a diameter of 3 inches. The company that

makes the cans uses sheets of metal that are 1,000 in?
3 in
Tomato
| 47 in
Soup

1. How many whole cans can the company make out of each sheet of metal?​

Answer 1

Number of whole cans with one sheet of metal: 18 cans

Leftover of metal: 24.535 in2

Explanation:

First we need to find the surface area of one can.

The surface area is calculated by:

S = 2*pi*r^2 + 2*pi*r*h

Where r is the radius and h is the height.

Using r = 3/2 = 1.5 and h = 4 1/4 = 4.25 (the value in the image), we have that:

S = 2*pi*1.5^2 + 2*pi*1.5*4.25 = 54.1925 in2

If the sheet of metal has 1000 in2, to find how many whole cans can be made with one sheet, we just need to divide the area of the sheet by the surface area of the can:

Number of cans = 1000 / 54.1925 = 18.4527 -> 18 cans

The leftover of metal is 1000 - 54.1925*18 = 24.535 in2

Answer 2

Explanation:

Given the volume of the metal sheet = 1000m³

Surface area of the cylindrical tin can = 2πr(r+h)

r is the radius

h is the height of the can

Given diameter = 2r

r = d/2 = 3/2 = 1.5in

h = 4 1/4in = 17/4 in

On substituting

S = 2(3.14)(1.5)(1.5+4.25)

S = 9.42×5.75

S = 54.17in²

The total amount of cans they can make out of the sheet metal = Area of the sheet/surface area of the tin can

= 1000/54.17

= 18.46

Approximately 18 whole cans

b) yes, there will be left over sheet of metal

Left over = Area of the sheet metal - (Surface Area of can × total number of tin can formed)

= 1000-(18×54.17)

= 1000 - 975.06

= 24.94in² of metal sheet will be left over