There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3

, what is the volume of the prism?(1 point)
Responses

16 in.3
  16 in. cubed

24 in.3
  24 in. cubed

96 in.3
  96 in. cubed

144 in.3
144 in. cubed
Skip to navigation

1 answer

The volume of a pyramid is given by the formula:

\[ V_{pyramid} = \frac{1}{3} \times B \times h \]

where \( B \) is the area of the base and \( h \) is the height. For a prism with the same base and height, the volume is given by:

\[ V_{prism} = B \times h \]

Since the base areas and heights are the same, we can relate the volumes of the pyramid and prism:

\[ V_{prism} = 3 \times V_{pyramid} \]

Given that the volume of the pyramid is \( 48 , \text{in}^3 \):

\[ V_{prism} = 3 \times 48 , \text{in}^3 = 144 , \text{in}^3 \]

Therefore, the volume of the prism is:

\[ \boxed{144 , \text{in}^3} \]