Question

max is building a model of a hotel that he is designing for a client. what is the volume of the model? the lower section, a rectangular prism, will hold all the hotel’s services. the upper section, a right triangular prism, will hold the hotel rooms.

Explanation:

Step1: Calculate volume of lower prism (rectangular prism)

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). Here, \( l = 10 \) in, \( w = 5 \) in, \( h = 3 \) in. So, \( V_{lower} = 10 \times 5 \times 3 = 150 \) cubic inches.

Step2: Calculate volume of upper prism (triangular prism)

The formula for the volume of a triangular prism is \( V = \frac{1}{2} \times b \times h_{triangle} \times l_{prism} \). The triangular base has legs \( 4 \) in and \( 9 \) in (right triangle), and the length of the prism is \( 10 \) in. So, \( V_{upper} = \frac{1}{2} \times 4 \times 9 \times 10 = 180 \) cubic inches.

Step3: Sum the volumes

Total volume \( V = V_{lower} + V_{upper} = 150 + 180 = 330 \) cubic inches.

Answer:

330