a cylinder vessel without a lid is made from a sheet of metal. Find the area of the metal required if the length of the vessel is 35 cm and it's radius is 14.
Circumference= 2πr
=2×(22/7)×14
=88
Area of circle = πr^2
=(22/7)×14×14
=616cm
Area of rectangle= l × B
=88×35
=3080cm^2
Area of metal required is 3080+ 616 = 3696sq.cm
find the area of the circle base first.
so:
A = πr²
= π(14)²
= 615.7521601
= 615.75 (2d.p.)
then,
SA = 2πr² + 2πrh
= 2(π(14)²) + 2π(14)(35)
= 4310.265121
= 4310.27 (2d.p)
A = 4310.27 - 615.75 (because we don't want to lid)
= 3694.52 (and that should be your answer)
IF YOU WANT A QUICKER WAY:
= πr² + 2πrh
and that should get you the same answer as above.
This is a really good clear, explantion Brea you are a great tutor his helped me too
3696
To find the area of the metal required to make the cylinder vessel, we need to calculate both the lateral surface area and the bottom area.
1. Lateral surface area: The formula for the lateral surface area of a cylinder is given by the equation A = 2πrh, where A represents the lateral surface area, π represents the mathematical constant pi (approximately 3.14159), r represents the radius of the cylinder, and h represents the height or length of the cylinder.
Given that the radius (r) is 14 cm and the length (h) is 35 cm, we can calculate the lateral surface area using the formula:
A = 2π(14)(35)
A ≈ 2(3.14159)(14)(35)
A ≈ 6154.56 cm²
2. Bottom area: The area of the bottom circle (which acts as the bottom of the cylinder) can be found using the formula A = πr^2.
Given that the radius (r) is 14 cm, we can calculate the bottom area using the formula:
A = π(14)^2
A ≈ 3.14159(14)^2
A ≈ 3.14159(196)
A ≈ 615.76 cm²
To find the total area of the metal required, we add the lateral surface area and the bottom area:
Total Area = Lateral Surface Area + Bottom Area
Total Area ≈ 6154.56 cm² + 615.76 cm²
Total Area ≈ 6770.32 cm²
Therefore, the area of the metal required to make the cylinder vessel is approximately 6770.32 cm².