Example 1
\(r = 3, h = 7 \rightarrow V = \pi(3^2)(7) = \pi(9)(7) \approx 197.92\) units³, \(SA = 2\pi(3^2) + 2\pi(3)(7) \approx 188.50\) units²
円柱計算機
半径と高さから円柱の体積と表面積を詳細なステップバイステップの解法で計算
結果
値を入力して計算をクリックして結果を表示してください。
Theory & Formula
A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. The volume represents the amount of space inside the cylinder.
The surface area consists of two parts: the area of the two circular bases (2πr²) and the lateral surface area that wraps around the sides (2πrh). When unrolled, the lateral surface forms a rectangle with dimensions 2πr (circumference) by h (height).
Properties and Applications
- The bases are congruent circles parallel to each other
- The lateral surface area = circumference × height = 2πrh
- If the height equals the diameter (h = 2r), it's called an equilateral cylinder
- Used to calculate volumes of cans, pipes, columns, and other cylindrical objects
- A cylinder is a prism with circular bases
\(V = \pi r^2 h, SA = 2\pi r^2 + 2\pi rh\)
Worked Examples
Example 2
\(r = 5, h = 10 \rightarrow V = \pi(5^2)(10) = \pi(25)(10) \approx 785.40\) units³, \(SA = 2\pi(5^2) + 2\pi(5)(10) \approx 471.24\) units²