Question

the three - dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. find the volume of the solid in cubic centimeters. diagram: a rectangular prism with length 20 cm, width 5 cm, height 5 cm, and a rectangular hole with length 20 cm, width 2 cm, height 2 cm inside it. options: 500 cubic centimeters, 420 cubic centimeters, 580 cubic centimeters, 180 cubic centimeters. there are buttons: submit, pass, dont know answer, save and close.

Explanation:

Step1: Calculate volume of outer prism

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). For the outer prism, \( l = 20 \) cm, \( w = 5 \) cm, \( h = 5 \) cm. So, \( V_{outer} = 20 \times 5 \times 5 = 500 \) cubic centimeters.

Step2: Calculate volume of the hole (inner prism)

The hole is also a rectangular prism with \( l = 20 \) cm, \( w = 2 \) cm, \( h = 2 \) cm. Using the volume formula, \( V_{hole} = 20 \times 2 \times 2 = 80 \) cubic centimeters.

Step3: Subtract hole volume from outer volume

To find the volume of the solid, we subtract the volume of the hole from the volume of the outer prism. So, \( V_{solid} = V_{outer} - V_{hole} = 500 - 80 = 420 \) cubic centimeters.

Answer:

420 cubic centimeters