Which will have a greater effect on the volume of the prism: doubling the height or doubling the width? Explain your reasons.
1 answer:
Doubling the width has a greater effect on volume.
The volume of a prism is calculated by this formula:
<span>Prism Volume = Area of Base • Height
The </span><span>Area of the Base </span>is calculated by this formula:
area = n * side² / (4*tan(180 / # of sides)
So, we see that doubling the width (the side length) will increase the volume by 4 whereas doubling the height only doubles the volume.
The volume of a prism is calculated by this formula:
<span>Prism Volume = Area of Base • Height
The </span><span>Area of the Base </span>is calculated by this formula:
area = n * side² / (4*tan(180 / # of sides)
So, we see that doubling the width (the side length) will increase the volume by 4 whereas doubling the height only doubles the volume.
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1 solution
Key:
Assume <em>x</em> is the the range x > 0 ≥ 1, in other words, assume <em>x</em> is equal to 1.
Step-by-step explanation: