Question

rectangular prism a has a volume of 275 cubic inches. rectangular prism b has the same dimensions as prism a except it is three times taller in height. what is the volume of prism b? 92 cu in. 278 cu in. 273 cu in, 825 cu in.

Explanation:

Step1: Recall volume formula for 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. For Prism A, let its volume be \( V_A = l \times w \times h_A = 275 \) cubic inches.

Step2: Determine volume of Prism B

Prism B has the same length and width as Prism A, but its height \( h_B = 3h_A \). So the volume of Prism B, \( V_B = l \times w \times h_B = l \times w \times 3h_A \). Since \( l \times w \times h_A = V_A = 275 \), we can substitute to get \( V_B = 3 \times V_A \).

Step3: Calculate \( V_B \)

Substitute \( V_A = 275 \) into the formula: \( V_B = 3 \times 275 = 825 \) cubic inches.

Answer:

825 cu in. (The option is the one with "825 cu in.")