Question

1. determine the surface area and volume of the following composite shapes. round all answers to the nearest tenth of a unit.

a) 4cm 4cm 4cm 4cm 12cm 4cm
b) 5 cm 3 cm

Explanation:

Step1: Volume of part a (base prism + cube)

Volume = (12×4×4) + (4×4×4) = 192 + 64 = 256 cm³

Step2: Surface area of part a (subtract overlapping areas)

Base SA: 2(12×4 + 12×4 + 4×4)=224; Cube SA: 6×4²=96; Overlap: 2×(4×4)=32
Total SA = 224 + 96 - 32 = 288 cm²

Step3: Volume of part b (cylinder + hemisphere, r=1.5cm, h=5cm)

Volume = π(1.5)²×5 + (2/3)π(1.5)³ = 11.25π + 2.25π = 13.5π ≈ 42.4 cm³

Step4: Surface area of part b (cylinder lateral + hemisphere curved + cylinder bottom)

SA = 2π×1.5×5 + 2π(1.5)² + π(1.5)² = 15π + 4.5π + 2.25π = 21.75π ≈ 68.3 cm²

Answer:

a) Surface Area: 288.0 cm², Volume: 256.0 cm³
b) Surface Area: 68.3 cm², Volume: 42.4 cm³