A plastic container is in the shape of an open cylinder. It has a lid cover which is also an open cylinder. The height of the lid is 2cm while the height of the container is 10m. If 8.2cm is for both, calculate. (a) the surface area of the container
(b) the surface area of the lid
(c) the total surface area of the plastic used to make both
Please help solve
the lateral area for a cylinder is 2πrh
the area of a circular face is πr^2
so now just plug in your numbers. Post your work if you get stuck.
Please help solve
Given:
Height of lid = 2 cm
Height of container = 10 cm
Diameter of both = 8.2 cm
To find:
a) Surface area of container
b) Surface area of lid
c) Total surface area of plastic used to make both
Solution:
Since the diameter of both the container and lid is 8.2 cm, the radius can be found by dividing it by 2:
r = d/2 = 8.2/2 = 4.1 cm
a) Surface area of container:
The surface area of the container consists of the lateral surface area and the circular base areas at both ends.
Lateral surface area = 2πrh = 2π(4.1)(10) = 820π/5 cm^2
Circular base area = πr^2 = π(4.1)^2 = 16.81π cm^2
Total surface area of container = Lateral surface area + 2 × Circular base area
= 820π/5 + 2 × 16.81π
= (820/5 + 33.62)π
= 200.52π
= 629.92 cm^2 (rounded off to two decimal places)
Therefore, the surface area of the container is approximately 629.92 cm^2.
b) Surface area of lid
The lid is a cylinder with height 2 cm and radius 4.1 cm.
Lateral surface area of lid = 2πrh = 2π(4.1)(2) = 16.4π cm^2
Circular top and bottom areas of lid = 2 × πr^2 = 2 × π(4.1)^2 = 33.62π cm^2
Total surface area of lid = Lateral surface area + Circular top and bottom areas
= 16.4π + 33.62π
= 50.02π
= 157.16 cm^2 (rounded off to two decimal places)
Therefore, the surface area of the lid is approximately 157.16 cm^2.
c) Total surface area of plastic used to make both
The total surface area of plastic used to make both the container and lid is the sum of the surface areas of the container and lid.
Total surface area = Surface area of container + Surface area of lid
= 629.92 + 157.16
= 787.08 cm^2 (rounded off to two decimal places)
Therefore, the total surface area of plastic used to make both the container and lid is approximately 787.08 cm^2.
To calculate the surface area of the container, we need to add up the areas of the curved surface (lateral surface area) and the areas of the two bases.
(a) Surface area of the container:
The curved surface area of a cylinder is given by the formula 2πrh, where π is a constant (approximated as 3.14), r is the radius, and h is the height.
Given that the height of the container is 10m and the additional height for the lid is 2cm, we have a total height of 10m + 0.02m = 10.02m.
Now, since the lid and container share the same radius, we need to subtract the height of the lid from the total height to get the height of the container alone: 10.02m - 0.02m = 10m.
Thus, the curved surface area of the container is 2πrh = 2 * 3.14 * r * 10m.
The area of each base of the container is given by the formula πr^2.
Therefore, the total surface area of the container is the sum of the curved surface area and twice the area of the base, which is 2πrh + 2πr^2.
(b) Surface area of the lid:
The surface area of the lid is equal to the curved surface area of a cylinder with a height of 2cm and radius r, which is given by 2πrh.
Since the additional height for the lid is 2cm, the height of the lid alone is 2cm - 0.02m = 0.02m.
Thus, the surface area of the lid is 2πrh = 2 * 3.14 * r * 0.02m.
(c) Total surface area of the plastic used to make both:
The total surface area is the sum of the surface area of the container and the surface area of the lid, which is 2πrh + 2πr^2 + 2πrh.
To calculate it, we can combine the common terms and get 4πrh + 2πr^2.
Now, in order to calculate the values, we need the radius of the plastic container. If you provide the radius, I can help you calculate the values using the given formulas.