Example 1
\(r = 3, h = 4 \rightarrow l = \sqrt{3^2 + 4^2} = 5, V = \frac{1}{3}\pi(3^2)(4) \approx 37.70\) units³, \(SA = \pi(3^2) + \pi(3)(5) \approx 75.40\) units²
円錐計算機
半径と高さから円錐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 cone is a three-dimensional shape with a circular base that tapers smoothly to a point called the apex or vertex. The volume of a cone is exactly one-third the volume of a cylinder with the same base and height.
The surface area consists of the base area (πr²) and the lateral surface area (πrl), where l is the slant height - the distance from the apex to any point on the circle's edge. The slant height can be found using the Pythagorean theorem: l = √(r² + h²).
Properties and Applications
- Volume of cone = 1/3 × Volume of cylinder with same base and height
- The slant height is always greater than the vertical height
- When unrolled, the lateral surface forms a sector of a circle
- Used to calculate volumes of ice cream cones, traffic cones, funnels, and conical structures
- A cone with apex directly above the center of the base is a right circular cone
\(V = \frac{1}{3}\pi r^2 h, SA = \pi r^2 + \pi rl, l = \sqrt{r^2 + h^2}\)
Worked Examples
Example 2
\(r = 5, h = 12 \rightarrow l = \sqrt{5^2 + 12^2} = 13, V = \frac{1}{3}\pi(5^2)(12) \approx 314.16\) units³, \(SA = \pi(5^2) + \pi(5)(13) \approx 282.74\) units²