To find area; what will be the formula of hollow cylinder if one side is closed?Explain
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Plz do not copy from any website... Explain it clearly.
Inappropriate ans will be reported....
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To find the area of a hollow cylinder with one side closed, we can break it down into two parts: the curved surface area and the area of the closed side.
1. Curved Surface Area:
The curved surface area of a hollow cylinder can be calculated by subtracting the inner curved surface area from the outer curved surface area.
Let's assume the outer radius of the cylinder is R and the inner radius is r. The height of the cylinder is h.
The formula for the outer curved surface area of a cylinder is:
A_outer = 2πRH
where π is a mathematical constant (approximately 3.14159), R is the outer radius, and H is the height.
The formula for the inner curved surface area of a cylinder is:
A_inner = 2πrh
where r is the inner radius.
So, the curved surface area of the hollow cylinder (excluding the closed side) is:
A_curved_surface = A_outer - A_inner
= 2πRH - 2πrh
= 2πh(R - r)
2. Area of the Closed Side:
The area of the closed side of the hollow cylinder is the same as the area of a circle with radius R (the outer radius).
The formula for the area of a circle is:
A_circle = πR²
Therefore , the total area of the hollow cylinder with one side closed is:
A_total = A_curved_surface + A_circle
= 2πh(R - r) + πR²
This formula takes into account both the curved surface area and the area of the closed side of the hollow cylinder.
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To find the area of a hollow cylinder with one side closed, we can break it down into two parts: the curved surface area and the area of the closed side.
1. Curved Surface Area:
The curved surface area of a hollow cylinder can be calculated by subtracting the inner curved surface area from the outer curved surface area.
Let's assume the outer radius of the cylinder is R and the inner radius is r. The height of the cylinder is h.
The formula for the outer curved surface area of a cylinder is:
A_outer = 2πRH
where π is a mathematical constant (approximately 3.14159), R is the outer radius, and H is the height.
The formula for the inner curved surface area of a cylinder is:
A_inner = 2πrh
where r is the inner radius.
So, the curved surface area of the hollow cylinder (excluding the closed side) is:
A_curved_surface = A_outer - A_inner
= 2πRH - 2πrh
= 2πh(R - r)
2. Area of the Closed Side:
The area of the closed side of the hollow cylinder is the same as the area of a circle with radius R (the outer radius).
The formula for the area of a circle is:
A_circle = πR²
Therefore , the total area of the hollow cylinder with one side closed is:
A_total = A_curved_surface + A_circle
= 2πh(R - r) + πR²
This formula takes into account both the curved surface area and the area of the closed side of the hollow cylinder.
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