A rectangle paper of 7cm is rolled along its widhth and a cylinder of ...
Given:
- The rectangle paper has a width of 7 cm.
To find:
- The volume of the cylinder formed when the paper is rolled along its width.
Solution:
Step 1: Calculate the length of the rectangle paper.
- The length of the rectangle paper is the circumference of the cylinder formed.
- The formula to calculate the circumference of a cylinder is:
Circumference = 2πr, where "r" is the radius of the cylinder.
- Given that the radius of the cylinder is 20 cm, substitute the value into the formula:
Circumference = 2π(20) = 40π cm.
Step 2: Calculate the length of the rectangle paper using the width and circumference.
- The rectangle paper is rolled along its width, so the length of the paper is equal to the circumference.
- Therefore, the length of the rectangle paper is 40π cm.
Step 3: Calculate the area of the rectangle paper.
- The area of a rectangle is given by the formula: Area = length × width.
- Substituting the values into the formula, we get:
Area = 40π cm × 7 cm = 280π cm².
Step 4: Calculate the volume of the cylinder.
- The volume of a cylinder is given by the formula: Volume = πr²h, where "r" is the radius and "h" is the height of the cylinder.
- In this case, the radius of the cylinder is 20 cm (given) and the height of the cylinder is equal to the width of the rectangle paper, which is 7 cm.
- Substituting the values into the formula, we get:
Volume = π(20 cm)² × 7 cm = 280π × 400 cm³ = 280,000π cm³.
Step 5: Simplify the volume.
- The value of π is approximately 3.14.
- Substituting the value of π into the volume equation, we get:
Volume ≈ 280,000 × 3.14 cm³ ≈ 879,200 cm³.
Answer:
- The volume of the cylinder formed when the rectangle paper is rolled along its width is approximately 879,200 cm³.
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