Geometry: Geometry: Geometry: Volume and Surface Area Formula Guide

📐 Volume and Surface Area Formula Guide 📏

Understanding volume and surface area is crucial in geometry. This guide provides formulas for common 3D shapes.

📦 Cube

• Volume (V): $V = a^3$, where $a$ is the side length.
• Surface Area (SA): $SA = 6a^2$

# Example Calculation
a = 5  # Side length
volume = a**3
surface_area = 6 * a**2
print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

🧱 Rectangular Prism

• Volume (V): $V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.
• Surface Area (SA): $SA = 2(lw + lh + wh)$

# Example Calculation
l, w, h = 5, 3, 4  # Length, width, height
volume = l * w * h
surface_area = 2 * (l*w + l*h + w*h)
print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

cylinder

• Volume (V): $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• Surface Area (SA): $SA = 2\pi r^2 + 2\pi rh$

# Example Calculation
r, h = 2, 5  # Radius, height
import math
volume = math.pi * r**2 * h
surface_area = 2 * math.pi * r**2 + 2 * math.pi * r * h
print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

🍦 Cone

• Volume (V): $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• Surface Area (SA): $SA = \pi r (r + \sqrt{h^2 + r^2})$

# Example Calculation
r, h = 3, 4  # Radius, height
import math
volume = (1/3) * math.pi * r**2 * h
surface_area = math.pi * r * (r + math.sqrt(h**2 + r**2))
print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

sphere

• Volume (V): $V = \frac{4}{3} \pi r^3$, where $r$ is the radius.
• Surface Area (SA): $SA = 4\pi r^2$

# Example Calculation
r = 4  # Radius
import math
volume = (4/3) * math.pi * r**3
surface_area = 4 * math.pi * r**2
print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

pyramid

• Volume (V): $V = \frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height.
• Surface Area (SA): $SA = B + \frac{1}{2}Pl$, where $B$ is the base area, $P$ is the base perimeter, and $l$ is the slant height.

# Example Calculation (Square Pyramid)
base_side = 4  # Side of the square base
h = 5  # Height
l = 6  # Slant height

B = base_side**2  # Base area
P = 4 * base_side  # Base perimeter

volume = (1/3) * B * h
surface_area = B + (1/2) * P * l

print(f"Volume: {volume}")
print(f"Surface Area: {surface_area}")

This guide provides fundamental formulas. Remember to use consistent units for accurate calculations. Happy calculating! 😃