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Sagot :
Answer:
4,895 containers
Step-by-step explanation:
The number of the wooden closed cylinders to be painted, n = 200
The diameter of each cylinder, d = 35 mm = 3.5 cm
The height of each cylinder, h = 7 cm
The surface area of each closed cylinder, A = 2·π·d²/4 + 2·π·(d/2)·h
Where, π = 3.142, we get;
A = 2 × 3.142 × 3.5²/4 + 2 × 3.142 × (3.5/2) × 7 = 96.22375
The surface area of each cylinder, A = 96.22375 cm²
The total surface area, [tex]A_T[/tex] = n × A
∴ [tex]A_T[/tex] = 200 × 96.22375 = 19,244.75
The total surface area that needs to be painted, [tex]A_T[/tex] = 19,22375 cm²
7. The base diameter of the tank, d₁ = 2.4 m = 240 cm
The height of the tank, h₁ = 6.4 m = 640 cm
The base radius of each cylinder container, r = 8.2 cm
The height of each cylindrical container, h₂ = 28 cm
The number of cylindrical containers which can be filled by the oil in the tank, n, is given as follows;
n = (The volume of the tank)/(The volume of a cylinder)
The volume of the tank, V₁ = π·(d²/4)·h₁
∴ V₁ = π × (240²/4) × 640 = 9216000·π
The volume of the tank, V₁ = 9216000·π cm²
The volume of a cylinder, V₂ = π·r²·h₂
∴ V₂ = π × 8.2² × 28 = 1,882.72·π
The volume of a cylinder, V₂ = 1,882.72·π cm²
The number of containers, n = 9216000·π/1882.72·π ≈ 4,895.045
Therefore, the number of complete cylindrical containers that can be filed by the oil in the tank, n = 4,895 containers
Answer:
6) About 19,244.75 square centimeters.
7) About 4895 containers.
Step-by-step explanation:
Question 6)
We need to paint 200 wooden closed cylinders of diameter 35 mm and height 7 cm. And we want to find the total surface area that needs to be painted.
First, since the diameter is 35 mm, this is equivalent to 3.5 cm.
The radius is half the diameter, so the radius of each cylinder is 1.75 cm.
Recall that the surface area of a cylinder is given by the formula:
Where r is the radius and h is the height.
Therefore, the surface area of a single cylinder will be:
Then the total surface area for 200 cylinders will be:
Question 7)
We know that the tank has a diameter of 2.4 m and a height of 6.4 m.
Since its diamter is 2.4 m, then its radius is 1.2 m.
Find the total volume of the tank. The volume for a cylinder is given by:
Since r = 1.2 and h = 6.4:
Each container has a base radius of 8.2 cm and a height of 28 cm.
So, the radius of each container is 0.082 m and the height is 0.28 m.
Then the volume of each container is:
Then to find the number of containers that can be filled by the tank, we can divide the two values. Hence:
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