Answer: a) 21 cans
b) 10.83 square inches.
Step-by-step explanation:
The cans are cylinders of 4 and 1/4 inches tall (or 4.25 in)
and the diameter is 3 inches.
The surface of a cylinder is equal to:
S = pi*r^2 + h*2*pi*r
where r is the radius, half of the diameter, so we have that r = 3in/2 = 1.5 in.
h is the height, h = 4.25 in
pi = 3.14
Then the surface needed for a can is:
S = 3.14*1.5^2 + 4.25*2*3.14*1.5 = 47.1 square inches.
if the sheet is 1000 in^2, we can make an amount of:
N = 1000/47.1 = 21.23
but we can not do a 0.23 of a can, so we need to round down.
A) we can make 21 cans out of a sheet of metal.
B) the 0.23 of a can that we removed earlier is the amount of metal leftover. The total is 0.23*47.1 in^2 = 10.83 in^2
Answer:
Step-by-step explanation:
To determine the amount of metal needed to make each can, we would determine the total surface area of each can. Since the cans are cylindrical, the formula for determining the total surface area of a cylinder is used. It is expressed as
Total surface area = πr² + 2πr
r = radius of the can
h = height of the can
π = 3.14
From information given,
Diameter = 4.25 inches
Radius = diameter/2 = 4.25/2 = 2.125 inches
Total surface area = 3.14 × 2.125² + 2 × 3.14 × 2.125 = 27.5 in²
1) since 1000 in² sheet material is available, the number of cans that can be made is
1000/27.5240625 = 36 cans
2) The amount of metal sheet left is
1000 - (36 × 27.5) = 10 in²
