MathIsimple

3D Geometry & Volumes

Master calculating volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres with real-world applications.

11th Grade
Geometry
~60 min
🎮 Interactive Activity: Volume Calculator

Calculate the volume of the 3D shape!

Shape: Rectangular Prism

Length: 5, Width: 4, Height: 3
🎮 Interactive Activity: Surface Area Calculator

Calculate the surface area of the 3D shape!

Shape: Rectangular Prism

Length: 5, Width: 4, Height: 3
1. Rectangular Prism Volume and Surface Area

Rectangular Prism Formulas

A rectangular prism (box) has length l, width w, and height h.

  • Volume: V = l × w × h
  • Surface Area: SA = 2(lw + wh + hl)
Example 1: Find Volume

Problem: A box has length 8 cm, width 5 cm, and height 3 cm. Find its volume.

Step 1: Identify dimensions: l = 8, w = 5, h = 3

Step 2: Apply formula: V = l × w × h = 8 × 5 × 3

Step 3: Calculate: V = 120

Answer: Volume = 120 cm³

Example 2: Find Surface Area

Problem: Same box. Find its surface area.

Step 1: SA = 2(lw + wh + hl)

Step 2: SA = 2(8×5 + 5×3 + 3×8) = 2(40 + 15 + 24)

Step 3: SA = 2(79) = 158

Answer: Surface Area = 158 cm²

2. Cylinder Volume and Surface Area
3. Cone Volume and Surface Area
4. Sphere Volume and Surface Area
5. Pyramid Volume and Surface Area
6. Composite Shapes
7. Real-World Applications
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
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Score
1
What is the volume of a rectangular prism with length 6, width 4, and height 3?
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2
What is the surface area of a cube with side length 5?
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3
What is the volume of a cylinder with radius 3 and height 5? (Use π ≈ 3.14)
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4
What is the surface area of a sphere with radius 4? (Use π ≈ 3.14)
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5
What is the volume of a cone with radius 3 and height 6? (Use π ≈ 3.14)
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6
A rectangular prism has dimensions 8 × 5 × 2. What is its surface area?
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7
What is the volume of a sphere with radius 5? (Use π ≈ 3.14)
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8
A cylinder has radius 2 and height 7. What is its total surface area? (Use π ≈ 3.14)
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9
What is the volume of a pyramid with base area 24 and height 8?
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10
A cube has volume 125. What is its surface area?
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