Question

student name: date: 5th grade cluster 2 assessment 2 1. what is the volume of this figure? a 16 cubic units b 83 cubic units c 140 cubic units d 150 cubic units 2. which expression could be used to find the volume of this rectangular prism? a 24×6 b 11×6 c 8 + 3 + 6 d 8×3 + 6 3. jennifer stacked 2 cubes on each square on this mat to form a rectangular prism. what is the volume of jennifers rectangular prism? a 125 b 50 c 25 d 20 length = 8 cm, width = 6 cm, height = 2 cm length = 12 cm, width = 3 cm, height = 12 cm length = 20 cm, width = 2 cm, height = 8 cm the volume of this figure? cubic inches

Explanation:

Step1: Count the number of cubes in each dimension

Assume each small cube has a volume of 1 cubic unit. For the first figure (question 1), if we count the number of cubes along length \(l = 7\), width \(w= 5\), and height \(h = 4\).

Step2: Use the volume formula for a rectangular prism \(V=l\times w\times h\)

Substitute \(l = 7\), \(w = 5\), and \(h=4\) into the formula \(V=7\times5\times4\).
First, calculate \(7\times5 = 35\). Then, \(35\times4=140\).

Step3: Analyze the second question (volume formula for rectangular prism \(V = l\times w\times h\))

For the second figure (question 2), assume the base - layer has \(l = 8\) and \(w = 3\) (number of unit - cubes in length and width of the base), and height \(h = 6\). The volume formula \(V=(l\times w)\times h=(8\times3)\times6 = 24\times6\)

Step4: Analyze the third question

For the third question (Jennifer's prism), count the number of squares on the mat. Assume the mat has \(l = 5\) and \(w = 5\) (number of squares in length and width). Since she stacks 2 cubes on each square, the height \(h = 2\). Using the volume formula \(V=l\times w\times h\), \(V = 5\times5\times2=50\)

Answer:

1. C. 140 cubic units
2. A. \(24\times6\)
3. B. 50