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
4 answers
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.
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.
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.