Question

which statement would give a correct method for finding the volume of the prism? she knows there are 30 unit cubes in the bottom layer. since the height is 4, there are 4 layers of 30 cubes each. she should multiply 4×30 = 120. the volume is 120 cubic units. she knows there are 11 cubes along the bottom and the height is 4, so she should multiply 4×11 = 44. the volume is 44 cubic units. she knows there are 30 unit cubes in the bottom layer she will need 4 more layers, so she should add 30+30+30+30+30 = 150. the volume is 150 cubic units. she knows there are 11 cubes along the bottom, and she needs 3 more layers. she has 33 cubes already in

Explanation:

Step1: Calculate the number of unit - cubes in one layer

The number of unit - cubes in one layer (bottom layer) is calculated by the formula \(l\times w\). Given \(l = 6\) and \(w=5\), the number of unit - cubes in one layer \(n=6\times5 = 30\).

Step2: Use the formula for the volume of a rectangular prism

The volume formula for a rectangular prism is \(V=B\times h\), where \(B\) is the area of the base (number of unit - cubes in one layer) and \(h\) is the height. Here, \(B = 30\) (unit - cubes in the bottom layer) and \(h = 4\) (number of layers). So \(V=30\times4\).

Answer:

She knows there are 30 unit cubes in the bottom layer. Since the height is 4, there are 4 layers of 30 cubes each. She should multiply \(4\times30 = 120\). The volume is 120 cubic units.