Lesson 21 Practice Problems1. A Scoop Of Ice Cream Has A 3-inch Diameter. How Tall Should The Ice Cream Cone Of The Same Diameter Be In Order To Contain All Of The Ice Cream Inside The Cone?

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Lesson 21 Practice Problems: Calculating the Height of an Ice Cream Cone

Understanding the Problem

When it comes to creating the perfect ice cream cone, the height of the cone is crucial in determining whether the ice cream will fit inside or spill over. In this problem, we are given a scoop of ice cream with a 3-inch diameter and asked to find the height of the ice cream cone with the same diameter that will contain all of the ice cream inside the cone.

The Concept of Similar Triangles

To solve this problem, we need to understand the concept of similar triangles. Similar triangles are triangles that have the same shape but not necessarily the same size. In this case, we can use the concept of similar triangles to find the height of the ice cream cone.

The Formula for the Height of a Cone

The formula for the height of a cone is given by:

h = (3/4) * r

where h is the height of the cone and r is the radius of the base of the cone.

Converting the Diameter to Radius

Since we are given the diameter of the ice cream scoop, we need to convert it to the radius. The radius is half of the diameter, so:

r = 3/2 = 1.5 inches

Calculating the Height of the Cone

Now that we have the radius, we can plug it into the formula to find the height of the cone:

h = (3/4) * 1.5 h = 1.125 inches

Conclusion

Therefore, the height of the ice cream cone with a 3-inch diameter that will contain all of the ice cream inside the cone is approximately 1.125 inches.

Real-World Applications

This problem may seem simple, but it has real-world applications in various fields such as architecture, engineering, and design. For example, in architecture, understanding the concept of similar triangles and the formula for the height of a cone can help designers create buildings with optimal proportions and stability.

Practice Problems

Here are some practice problems to help you reinforce your understanding of the concept:

  1. A cone has a base radius of 4 inches and a height of 6 inches. What is the diameter of the base?
  2. A cone has a base diameter of 6 inches and a height of 8 inches. What is the radius of the base?
  3. A cone has a base radius of 2 inches and a height of 4 inches. What is the diameter of the base?

Answer Key

  1. The diameter of the base is 8 inches.
  2. The radius of the base is 3 inches.
  3. The diameter of the base is 4 inches.

Additional Resources

For more practice problems and resources, check out the following links:

Conclusion

In conclusion, calculating the height of an ice cream cone is a simple problem that requires understanding the concept of similar triangles and the formula for the height of a cone. By applying these concepts, we can create the perfect ice cream cone that will contain all of the ice cream inside.