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Circle Lock

Escape: open the lock · 6 items · by claraputriy
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What’s inside

Solve each geometry question to open the combination lock.

  1. What is the standard equation of a circle with center $(0,0)$ and radius $r = 5$? (Remember the Pythagorean theorem in the coordinate plane.)
    x + y = 25 · x^2 + y^2 = 5 · x^2 + y^2 = 25 · x^2 - y^2 = 25
  2. Find the radius of a circle given the equation $(x - 2)^2 + (y + 3)^2 = 49$. (The right side of the standard equation equals the radius squared.)
    3 · 7 · 14 · 49
  3. What are the coordinates of the center of the circle $(x + 4)^2 + (y - 1)^2 = 36$? (Change the signs of the numbers inside the parentheses.)
    (-4, -1) · (-4, 1) · (4, -1) · (4, 1)
  4. What is the diameter of a circle if its radius measures $9$ cm? (The diameter is twice the length of the radius.)
    4.5 cm · 9 cm · 18 cm · 81 cm
  5. What is the circumference of a circle with a radius of $5$ units? (Use $\pi$) (The formula for the circumference is $C = 2\pi r$.)
    5\pi · 10\pi · 20\pi · 25\pi
  6. Find the area of a circle with a radius of $4$ units. (Use $\pi$) (The formula for the area is $A = \pi r^2$.)
    4\pi · 8\pi · 16\pi · 32\pi
Answer key
  1. What is the standard equation of a circle with center $(0,0)$ and radius $r = 5$? → x^2 + y^2 = 25
  2. Find the radius of a circle given the equation $(x - 2)^2 + (y + 3)^2 = 49$. → 7
  3. What are the coordinates of the center of the circle $(x + 4)^2 + (y - 1)^2 = 36$? → (-4, 1)
  4. What is the diameter of a circle if its radius measures $9$ cm? → 18 cm
  5. What is the circumference of a circle with a radius of $5$ units? (Use $\pi$) → 10\pi
  6. Find the area of a circle with a radius of $4$ units. (Use $\pi$) → 16\pi
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