Geometric Shapes and Formulas

Study Notes

Geometric Shapes

Circle:
- Area formula: A = πr², where r is the radius.
- Circumference formula: C = 2πr, measuring the distance around the circle.
Square:
- Area calculation: A = length x length, which simplifies to A = a².
- Perimeter formula: P = 4a, representing the total distance around the square.
Rectangle:
- Area is determined by A = length x breadth, represented as A = ab.
- Perimeter is calculated using P = 2a + 2b, accounting for both lengths and widths.

3D Shapes

Right Cylinder:
- Volume is calculated with the formula V = πr² x h, where r is the radius and h is height.
- Surface area is given by SA = 2πr² + 2πrh, covering top, bottom, and the curved surface area.
Square Prism (Cube):
- Volume formula: V = a² x H, noting that height (H) equals side length (a) if square.
- Simplified volume: V = a³.
- Surface area: SA = 6a², reflecting all six square faces.
Square Base Pyramid:
- Volume calculated as V = 1/3 a² x H, where 'a' is the base side length and 'H' is the height.
- Surface area: SA = area of square base (a²) + 4 times the area of a triangle side; simplifies to SA = a² + 2ah, with 'h' as the triangle height.
Rectangular Prism (Cuboid):
- Volume determined by V = l x b x h, multiplying length, breadth, and height.
- Surface area formula: SA = 2lb + 2lh + 2bh, accounting for all six rectangular faces.
Slant Height:
- Defined as the line from the midpoint of the base edge to the apex of the pyramid.
- Calculation uses Pythagorean Theorem, assessing the perpendicular height and base dimensions.

Description

Test your knowledge on geometric shapes, including both 2D and 3D figures. This quiz will cover formulas for area, perimeter, volume, and surface area of circles, squares, rectangles, cylinders, prisms, and pyramids. Challenge yourself to apply these formulas correctly!