Calculating the Volume of a Hollow Iron Roller for SEO
When dealing with mathematical problems, understanding how to calculate the volume of a hollow object is crucial in various applications, including engineering and manufacturing. This article explores a specific problem involving a hollow iron roller and provides step-by-step solutions using the formula for volume of a hollow cylinder, which is highly relevant for SEO purposes. By breaking down the problem and presenting it in a clear, concise manner, this content can help optimize a webpage for better search engine performance.
Problem Definition
A hollow iron roller of length 63 cm and having a girth of 440 cm has a thickness of 4 cm. The objective is to calculate the volume of metal used for making the roller.
Step 1: Identifying the Given Values
The given values are:
Length (h) of the roller: 63 cm Girth of the roller: 440 cm (which is equivalent to the circumference of the roller) Thicknes of the roller: 4 cmStep 2: Calculating the Internal Radius
The girth (circumference) of the roller is given by the formula:
Circumference 2πr
Where 'r' is the internal radius. We can rearrange this formula to find 'r':
r Girth / (2π)
Given that the girth is 440 cm:
r 440 cm / (2 × π) 440 cm / (2 × 22/7)
r 440 × 7 / 44 70 cm
Step 3: Calculating the External Radius
The thickness of the roller is 4 cm. Therefore, the external radius (R) is:
R r thickness 70 cm 4 cm 74 cm
Step 4: Volume of the Hollow Roller
The volume of a hollow cylinder is given by the formula:
Volume πh (R2 - r2)
Substituting the values into the formula:
Volume (22/7) × 63 cm × [(74 cm)2 - (70 cm)2]
Volume (22/7) × 63 cm × [5476 cm2 - 4900 cm2]
Volume (22/7) × 63 cm × 576 cm2
Volume 22 × 63 × 576 / 7 22 × 864 19008 cm3
Answer
The volume of metal used for making the hollow roller is 19008 cubic centimeters.
SEO Optimization for Content
This article can be optimized for SEO by including relevant keywords, headings, and meta tags. The primary keyword should be "hollow roller," which appears frequently in the content and is highly relevant to the audience. Other related keywords such as "volume calculation" and "mathematical problem" can also be used to enhance the page's rank in search engine results pages (SERPs).
Metatags and headers should include:
Title Tag: Calculating the Volume of a Hollow Iron Roller for SEO Description Tag: Learn how to calculate the volume of a hollow roller using the formula for the volume of a hollow cylinder, enhancing your SEO knowledge.Calculating the Volume of a Hollow Iron Roller for SEO
Problem Definition
Step-by-Step Solution
SEO Optimization for Content
This content not only provides a clear and accurate solution to the given mathematical problem but also optimizes the webpage for better search engine visibility.