Answer:
The surface area of the decorative block is 253.68 cm²
Step-by-step explanation:
The decorative block is a composite figure comprising of the following parts;
1) A solid cube with side length, S = 6 cm
2) A hemisphere with diameter, D = 4 cm
The surface area of the decorative block = The surface area of the solid cube + The surface area of the hemisphere
The surface area of the components of the decorative block are as follows;
The surface area of the solid cube = 6 × S² = 6 × (6 cm)² = 216 cm²
The surface area of the hemisphere = π·D²/4 + π·D²/2
∴ The surface area of the hemisphere = 3.14 × (4 cm)²/4 + 3.14 × (4 cm)²/2 = 37.68 cm²
∴ The surface area of the decorative block = 216 cm² + 37.68 cm² = 253.68 cm².
