Surface Areas and Volumes | Class 10 Mathematics Notes

Examples on Surface Area of Combination of Solids

This section provides detailed worked examples illustrating the calculation of surface areas for various combined solids.

Example 1 involves a playing top shaped like a cone surmounted by a hemisphere with a total height of 5 cm and diameter 3.5 cm. The curved surface area of the hemisphere is calculated as 2πr², and the slant height of the cone is found using the Pythagorean theorem as l = √(r² + h²). The total surface area is the sum of the curved surface areas of the hemisphere and the cone, resulting in approximately 39.6 cm².

Example 2 considers a decorative block made of a cube with edge 5 cm and a hemisphere of diameter 4.2 cm fixed on top. The total surface area is calculated by subtracting the base area of the hemisphere from the cube's surface area and adding the curved surface area of the hemisphere, yielding approximately 163.86 cm².

Example 3 features a wooden toy rocket shaped like a cone mounted on a cylinder with different base diameters. The surface areas painted orange (cone) and yellow (cylinder) are calculated separately using the formulas for curved surface areas and areas of circular bases, taking care to subtract overlapping areas where necessary. The orange area is approximately 63.585 cm², and the yellow area is approximately 195.465 cm².

Example 4 involves a bird-bath shaped like a cylinder with a hemispherical depression at one end. The total surface area is the sum of the curved surface areas of the cylinder and hemisphere, calculated as 2πr(h + r), resulting in 3.3 m².

These examples emphasize the importance of understanding which surfaces are visible and which are hidden, and applying the correct formulas accordingly.

📊 Diagram: Fig. 12.6; Fig. 12.7; Fig. 12.8; Fig. 12.9

🧪 Activity: Step-by-step calculation of surface areas for combined solids using given dimensions.

🔗 Connection: Leads to the next section on volume calculations of combined solids.