To calculate the volume of a rectangular prism, use the formula V = l × w × h, where l is the length, w is the width, and h is the height. For example, if a prism has a length of 5 cm, width of 3 cm, and height of 10 cm, the volume will be 150 cm³.
For surface area, use the formula A = 2lw + 2lh + 2wh, which adds up the areas of all six faces. In the same example, the surface area would be 2(5 × 3) + 2(5 × 10) + 2(3 × 10) = 150 cm².
To calculate the volume of a sphere, use V = (4/3)πr³, where r is the radius. For a sphere with a radius of 7 cm, the volume is approximately 1436.76 cm³.
3D Geometric Figure Practice Problems
To find the volume of a cone, use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. For a cone with a radius of 4 cm and a height of 9 cm, the volume will be 150.8 cm³.
For the surface area of a cylinder, use A = 2πr² + 2πrh, where r is the radius and h is the height. If the cylinder has a radius of 5 cm and a height of 10 cm, the surface area is 471.2 cm².
For a pyramid, the volume is V = (1/3) × Base Area × Height. If the base area of the pyramid is 20 cm² and the height is 12 cm, the volume will be 80 cm³.
How to Calculate Volume and Surface Area of 3D Figures
For a rectangular prism, the volume is calculated using the formula V = l × w × h, where l is length, w is width, and h is height. If a rectangular prism has dimensions 6 cm by 3 cm by 4 cm, the volume is 72 cm³.
The surface area of a rectangular prism is calculated with the formula A = 2lw + 2lh + 2wh. For a prism with a length of 6 cm, width of 3 cm, and height of 4 cm, the surface area is 2(6 × 3) + 2(6 × 4) + 2(3 × 4) = 108 cm².
For a cylinder, the volume is V = πr²h, where r is the radius and h is the height. If a cylinder has a radius of 5 cm and a height of 10 cm, the volume is 785.4 cm³.
To find the surface area of a cylinder, use the formula A = 2πr² + 2πrh. For the same cylinder, the surface area is 2π(5²) + 2π(5)(10) = 471.2 cm².
Steps for Identifying and Classifying 3D Geometric Figures
First, examine the number of faces. A figure with six rectangular faces is a rectangular prism, while a figure with a circular base and a pointed top is a cone. If a figure has a round base and straight sides extending up, it is a cylinder.
Next, check the edges. A pyramid has triangular faces and a polygonal base, while a sphere has no edges. A cube is a special case of a rectangular prism where all faces are squares, and each edge is equal in length.
Consider symmetry. Figures with multiple equal faces, like a regular tetrahedron or octahedron, are classified as polyhedra. If a figure has rotational symmetry around a central axis, it is likely a cone, cylinder, or sphere.
Finally, count the vertices. A cube has 8 vertices, while a triangular prism has 6. Understanding the number and arrangement of vertices can help distinguish between similar shapes like a rectangular prism and a cube.