Calculating the Number of Times a Smaller Cylinder Can Be Poured Into a Larger Cylinder: A Comprehensive Guide

Have you ever wondered how many times a smaller cylindrical tank can be completely poured into a larger one? This question often arises in various practical applications, such as in the design and operation of water storage tanks or in industrial processes where fluid distribution is crucial. In this article, we will explore the mathematical behind this calculation using concrete examples and provide a detailed methodology.

Introduction to Cylinder Volume Calculation

A cylinder's volume can be calculated using the formula:

Volume πr2h, where r is the radius and h is the height.

This formula is fundamental in understanding the relationship between the dimensions of a cylinder and its volume. By knowing the volumes of both the smaller and larger cylinders, we can determine how many times the smaller cylinder can be poured into the larger one.

Problem Statement and Solution

The problem at hand involves two cylindrical tanks:

Small Cylinder (SCT): Radius 2 m, Height 3 m Large Cylinder (LCT): Radius 5 m, Height 12 m

The goal is to find out how many times the small cylinder can be poured into the large cylinder.

Volume Calculation for Small Cylinder (SCT)

First, let's calculate the volume of the small cylinder:

VolumeSCT πr2h π(22)3 12π m3

Volume Calculation for Large Cylinder (LCT)

Next, we calculate the volume of the large cylinder:

VolumeLCT πr2h π(52)12 300π m3

Calculating the Number of Times

To determine how many times the small cylinder can be poured into the large one, we divide the volume of the large cylinder by the volume of the small cylinder:

Number of Times VolumeLCT / VolumeSCT 300π m3 / 12π m3 25

Therefore, the large cylinder can be filled 25 times with the contents of the small cylinder.

Explanation of the Calculation

The solution can also be explained through the proportional relationship between the volumes and the dimensions of the cylinders:

Height proportion: The large cylinder is 4 times taller than the small one (12/3 4). Radius proportion: The area of the base of the large cylinder is 6.25 times that of the small one (52/22 25/4 6.25).

The overall increase in volume due to both the height and the base area is thus 25 times. This is why the larger cylinder can hold 25 times the volume of the smaller cylinder.

Conclusion

Understanding the relationship between the dimensions and volumes of cylindrical tanks is crucial in many practical applications. The example provided in this article demonstrates a step-by-step approach to solving such problems, which can be applied to a wide range of scenarios involving fluid distribution and volume calculations.

For more information on similar topics, exploring the volume calculations for other shapes and volumes in related fields such as engineering, environmental science, or industrial design can provide valuable insights.

Keywords: cylinder volume calculation, tank volume, fluid distribution