You need to make a soda can with a volume of 29 cubic inches.
Find the surface area. calculate the following:
a) How much material is needed if the can's radius is 2 inch?
Answer with the help of Reiny,
but doing it with a different radius
to make sure I got it.
let the height be h
volume = ðr^2h
ð(2^2)h = 29
h = ð/29
the surface area are
top + bottom + rectangle forming the outside of the cylinder
= 2ðr^2 + 2ðrh
= 2P(2) + 2ð(2)(ð/29)
= 54.13274 in^2
Since
Top = 12.56637 in^2
Bottom = 12.56637 in^2
Total surface if can radius is 2inch is: A = 54.13274 in^2
sorry:
ð = pi
After
2πr^2 + 2πrh , if r = 2, you forgot to square the 2 in the first term, should have been
2π(4) + 2π(2)29/π)
Make the necessary changes in your calculations
(I got 26.49)
BTW, even with your error how does
2π(2) + 2π(2)(π/29) = 54.13
I had 13.93
the first term of 2πr^2 is the sum of the top and bottom, since each is a circle of πr^2 )
To calculate the surface area of the soda can with a different radius, we can follow the same steps as explained by Reiny.
1. Let's assume the radius of the can as 4 inches. We already know the volume of the can is 29 cubic inches.
2. Using the formula for the volume of a cylinder, which is V = πr²h, we can substitute the values:
π(4²)h = 29
16πh = 29
h = 29 / (16π)
h ≈ 0.5745 inches (rounded to four decimal places)
3. Now, let's calculate the surface area of the can. It consists of the top, the bottom, and the rectangle forming the outside of the cylinder.
4. The surface area of the top and bottom can be found using the formula for the area of a circle, which is A = πr². Since the radius is 4 inches, the area of each circle is:
A(top) = π(4²) ≈ 50.2655 square inches
A(bottom) = π(4²) ≈ 50.2655 square inches
5. The surface area of the rectangle can be found using the formula A = 2πrh. Since the radius is 4 inches and the height is 0.5745 inches, the area of the rectangle is:
A(rectangle) = 2π(4)(0.5745) ≈ 14.4227 square inches
6. Finally, we can find the total surface area by adding the areas of the top, bottom, and rectangle:
Total surface area = A(top) + A(bottom) + A(rectangle)
≈ 50.2655 + 50.2655 + 14.4227
≈ 114.9537 square inches
Therefore, if the radius of the soda can is 4 inches, the total surface area needed would be approximately 114.9537 square inches.