Question

how does the area of the base affect the volume of a prism or cylinder?
a. it has no effect
b. a larger base area results in a smaller volume
c. only the height affects the volume
d. a larger base area results in a larger volume

Explanation:

Step1: Recall the volume formula

The volume formula for a prism or cylinder is \(V = B\times h\), where \(B\) is the base area and \(h\) is the height.

Step2: Analyze the relationship

If the height \(h\) is constant (assuming no change in height), when \(B\) increases (larger base area), since \(V\) is the product of \(B\) and \(h\), \(V\) will increase. For example, if \(h = 5\), \(B_1= 2\), then \(V_1=2\times5 = 10\); if \(B_2 = 3\), then \(V_2=3\times5=15\).

Answer:

d. A larger base area results in a larger volume