Final answer:
The volume of the rectangular prism shaped gift bag is 750 cm³ and the surface area is 550 cm². The shape affects its capacity to hold items efficiently and has an impact on its presentation by providing a stable base and pleasing form.
Step-by-step explanation:
Understanding the Volume and Surface Area of a Rectangular Prism
To calculate the volume of a rectangular prism, which in this context is the gift bag with dimensions 10 cm x 5 cm x 15 cm, the formula to use is length × width × height. Therefore, the volume (V) is calculated as follows:
V = 10 cm × 5 cm × 15 cm = 750 cm³.
The surface area, which is the sum of the areas of all the faces of the prism, requires a different formula: 2(length × width) + 2(length × height) + 2(width × height). Using the provided dimensions:
Surface Area (SA) = 2(10 cm × 5 cm) + 2(10 cm × 15 cm) + 2(5 cm × 15 cm) = 100 cm² + 300 cm² + 150 cm² = 550 cm².
The shape of the gift bag affects its capacity in terms of the volume it can hold. Since the bag is a rectangular prism, it might provide efficient packing space with less wasted volume compared to other shapes. Additionally, the shape can impact presentation by providing a stable base for ease of display and an aesthetically pleasing geometric form.