Pyramid, Tetrahedron, Frustum, and Solid Geometry

---

Pyramid

Volume = $\frac {1} {3}$× base area × height Slant height (l) = √(R² + h²)

Lateral surface area = $\frac{1}{2}$× perimeter × slant height

---

Tetrahedron

For a regular tetrahedron with side a:

Height = (√6 / 3) × a

Base center to vertex = a / √3

Volume = (√2 / 12) × a³

---

Frustum

For a frustum with top radius r, bottom radius R, and height h:

Slant height (l) = √(h² + (R − r)²)

Curved surface area = π(R + r)l

Total surface area = π(R + r)l + πR² + πr²

Volume = (1/3) × π × h × (r² + R² + rR)

Sphere

Surface area = 4πr²

Volume = (4/3)πr³

For r = 7: Surface area = 154, Circumference = 44

For r = 14: Surface area = 616, Circumference = 88

---

Cylinder

Volume = πr²h

Curved surface area = 2πrh

Relation: Volume = (1/2) × Curved surface area × r

---