Question

a rectangular prism has a volume of 24 cm³. if the height of the prism triples, and the other two dimensions stay the same, what is the new volume? 48 cm³ 72 cm³ 8 cm³ 12 cm³

Explanation:

Step1: Recall volume formula of rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Initially, \( V_1 = l \times w \times h_1 = 24\ \text{cm}^3 \).

Step2: Analyze new volume with tripled height

When the height triples, the new height \( h_2 = 3h_1 \), and length \( l \) and width \( w \) remain the same. So the new volume \( V_2 = l \times w \times h_2 = l \times w \times 3h_1 \).

Step3: Relate new volume to original volume

Since \( l \times w \times h_1 = 24\ \text{cm}^3 \), we can substitute this into the formula for \( V_2 \). So \( V_2 = 3\times(l \times w \times h_1)= 3\times24 \).

Step4: Calculate new volume

\( 3\times24 = 72\ \text{cm}^3 \).

Answer:

\( 72\ \text{cm}^3 \) (corresponding to the option: \( 72\ \text{cm}^3 \))