Center at Origin: Real-world Applications in Architecture & Design
Mathematics
Grade 7
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet explores circle equations with centers at the origin through architecture and design contexts. Students will practice procedural skills, solve multi-step problems, and analyze real-world applications.
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Center at Origin: Real-world Applications in Architecture & Design
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Calculate the radius and write the equation of the circle centered at the origin for each scenario. Show all working in the grid spaces provided.
1.
A circular fountain in a park has a radius of 5 meters. Write the equation of the circle centered at the origin.
[2 marks]2.
The radius of a circular plaza is 8 meters. Find its equation.
[2 marks]3.
Calculate the radius of a circle with equation x^2 + y^2 = 49.
[2 marks]4.
Given the circle x^2 + y^2 = 100, what is its radius?
[2 marks]B
Problem Solving & Reasoning
Solve these multi-step problems involving circles centered at the origin. Show your reasoning in the grid space.
1.
An architect designs a circular window with a radius of 6 meters. If the window is centered at the origin, write its equation and determine the area of the window.
[4 marks]2.
A circular sculpture is placed at the origin with an equation x^2 + y^2 = 64. If a design element extends 3 meters beyond the sculpture's boundary, what is the equation of the outer boundary?
[4 marks]3.
A circular arch in a building has radius 4 meters. If the arch's bottom is at ground level and its center is at height 4 meters, write its equation assuming the center is at (0,4).
[3 marks]C
Real-world Applications
Apply your understanding of circle equations to design and architecture scenarios. Show calculations and reasoning clearly.
1.
An architect is designing a circular garden with a radius of 9 meters, centered at the origin. The design includes placing a circular fountain at the center. Write the equation of the fountain's boundary.
[3 marks]2.
A circular skylight in a ceiling has a radius of 2.5 meters. The center of the skylight is at the origin. Write its equation and find the diameter of the skylight.
[3 marks]3.
Design a circular decorative element with a radius of 3 meters at the origin in a mural. Write its equation and calculate its circumference.
[4 marks]D
Challenge & Extension
Tackle these advanced problems involving circles centered at the origin. Show detailed reasoning.
1.
A design requires a circular feature with a radius that is 1.5 times the radius of a smaller circle with equation x^2 + y^2=25. Write the equation of the larger circle.
[4 marks]2.
If a circle at the origin has an equation x^2 + y^2 = r^2 and a point (3,4) lies on this circle, find the radius r and write the equation.
[4 marks]E
Mixed Review
Answer these varied questions to review your understanding of circles centered at the origin.
1.
Identify and correct the mistake in this equation of a circle centered at the origin: x^2 + y^2= -16.
[2 marks]2.
Explain why the equation x^2 + y^2 = 0 represents a circle of radius zero.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet