Question

Understanding: Two pillars have been delivered for the support of a shade structure in the backyard. They are both 10 feet tall, but unfortunately, the makers of the pillars did not create the same-shaped pillars. In two to three sentences, describe steps you can take to determine whether the pillars have the same volume.

a) Measure the circumference of each pillar at regular intervals and compare the measurements.
b) Calculate the surface area of each pillar and check for equality.
c) Determine the base area of each pillar and compare the results.
d) Calculate the volume of each pillar and compare the results.

Answer 1

To compare the volumes of two pillars of constant height, calculate the base area of each and then their volumes using the respective geometrical formulas, such as V = πr²h for cylinders.

Step-by-step explanation:

To determine whether two pillars have the same volume, you should measure attributes that directly relate to volume. Specifically:

1. Calculate the base area of each pillar, as knowing the area of the base can help you determine the volume if the height is the same, which is the case for these pillars.
2. Calculate the volume of each pillar based on their geometrical shape. For pillars that are cylindrical, you would use the formula V = πr²h, where r is the radius and h is the height. For other shapes, you would use the respective volume formula for that shape and compare the results.

Measuring circumference alone (option a) or calculating surface area (option b) would not provide sufficient information about volume. Option c) provides partial information, which in this scenario could be enough given that the height is constant for both pillars. Option d) is the most direct and conclusive approach to ensure the volumes are equal.