1. What are Volume and Surface Area Formulas?

Definition: These formulas calculate the space occupied by 3D shapes (volume) and the total area of their surfaces (surface area).

Purpose: Essential for engineering, construction, manufacturing, and any field dealing with three-dimensional objects.

2. Common Volume Formulas

• Cube: \( V = s^3 \) (s = side length)
• Rectangular Prism: \( V = L \times W \times H \)
• Cylinder: \( V = \pi r^2 h \)
• Sphere: \( V = \frac{4}{3}\pi r^3 \)
• Cone: \( V = \frac{1}{3}\pi r^2 h \)

3. Common Surface Area Formulas

• Cube: \( SA = 6s^2 \)
• Rectangular Prism: \( SA = 2(LW + LH + WH) \)
• Cylinder: \( SA = 2\pi r(r + h) \)
• Sphere: \( SA = 4\pi r^2 \)
• Cone: \( SA = \pi r(r + \sqrt{h^2 + r^2}) \)

4. Using the Calculator

Steps:

1. Select the shape from the dropdown
2. Enter the required dimensions
3. Click Calculate to get volume and surface area

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units (all in meters, feet, etc.). Results will be in cubic units for volume and square units for surface area.

Q2: How accurate are these calculations?
A: These are theoretical values for perfect geometric shapes. Real-world objects may vary.

Q3: Can I calculate for irregular shapes?
A: No, this calculator only handles regular geometric shapes with known formulas.

Q4: Why is π (pi) used in circular shapes?
A: Pi is the ratio of a circle's circumference to its diameter, essential for calculations involving circular bases or surfaces.

Q5: How do I measure radius if I only have diameter?
A: Radius is half the diameter. Divide your diameter measurement by 2 before entering.