Geometry Chapter 12: Arcs and Solid Figures

Solid Figures

• Solids are objects having a definite shape, size, and occupy a fixed amount of space in three dimensions.
• Examples of solid figures include cube, cuboid, cylinder, cone, sphere, and hemisphere.

Surface Areas

• Surface Area (SA) is the area of all surfaces of a solid body together, measured in square units.
• Total Surface Area (TSA) of a cube = 6a² sq units, where a is the edge of the cube.

Cuboid

• A cuboid is a solid figure having 6 rectangular faces.
• Let its length = l units, breadth = b units, and height = h units.
• Total Surface Area (TSA) of a cuboid = 2(lb + lh + bh) sq units.
• Lateral Surface Area (LSA) of a cuboid = 2(lb + bh) sq units.
• Diagonal of a cuboid = √(l² + b² + h²) units.
• Volume of a cuboid = l × b × h cu units.

Cube

• A cube is a special case of a cuboid with square faces.
• Total Surface Area (TSA) of a cube = 6a² sq units.
• Lateral Surface Area (LSA) of a cube = 4a² sq units.
• Diagonal of a cube = √3a units.
• Volume of a cube = a³ cu units.

Right Circular Cylinder

• A cylinder is a solid figure obtained by revolving a rectangle about its one side.
• Let base radius of the cylinder be r units and its height be h units.
• Curved Surface Area (CSA) of a cylinder = 2πrh sq units.
• Total Surface Area (TSA) of a cylinder = 2πrh + 2πr² sq units.
• Volume of a cylinder = πr²h cu units.

Right Circular Hollow Cylinder

• Let R units and r units be the external and internal radii of the hollow cylinder, respectively, and h units be its height.
• Curved Surface Area (CSA) of a hollow cylinder = 2π(R + r)h sq units.
• Total Surface Area (TSA) of a hollow cylinder = 2π(R + r)h + 2π(R² - r²) sq units.
• Volume of a hollow cylinder = π(R² - r²)h cu units.

This quiz covers concepts related to arcs, angles, and the areas of solid figures such as cubes, cylinders, cones, and spheres. Topics include calculating arc lengths, finding missing angles, and determining surface areas and volumes of various solid objects.