Question

problem 6c
nekeisha says that calculating the volume of this rectangular prism is the same as calculating the volume of five 1×3×2 - centimeter prisms added together.
is this true?
true false not enough information
(image of a rectangular prism with height 5 cm, length 3 cm, width 2 cm)

Explanation:

Step1: Calculate volume of main prism

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). For the given prism, \( l = 3 \) cm, \( w = 2 \) cm, \( h = 5 \) cm. So, \( V_{\text{main}} = 3 \times 2 \times 5 = 30 \) \( \text{cm}^3 \).

Step2: Calculate volume of five small prisms

For a small prism with dimensions \( 1 \times 3 \times 2 \) cm, its volume is \( V_{\text{small}} = 1 \times 3 \times 2 = 6 \) \( \text{cm}^3 \). Five such prisms will have a total volume of \( 5 \times 6 = 30 \) \( \text{cm}^3 \).

Step3: Compare the two volumes

Since \( V_{\text{main}} = 30 \) \( \text{cm}^3 \) and the total volume of five small prisms is also \( 30 \) \( \text{cm}^3 \), Nekeisha's statement is true.

Answer:

True