Apply Circle Area and Circumference Formulas - 7th Grade Math
Card 1 of 25
Find the radius when the area is $A = 49\pi$.
Find the radius when the area is $A = 49\pi$.
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$r = 7$. From $A = \pi r^2$: $49\pi = \pi r^2$, so $r^2 = 49$, thus $r = 7$.
$r = 7$. From $A = \pi r^2$: $49\pi = \pi r^2$, so $r^2 = 49$, thus $r = 7$.
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Find the radius when the diameter is $d = 18$.
Find the radius when the diameter is $d = 18$.
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$r = 9$. Use $r = \frac{d}{2}$ with $d = 18$: $r = \frac{18}{2} = 9$.
$r = 9$. Use $r = \frac{d}{2}$ with $d = 18$: $r = \frac{18}{2} = 9$.
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Find the area when $r = 5$ (leave the answer in terms of $\pi$).
Find the area when $r = 5$ (leave the answer in terms of $\pi$).
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$25\pi$. Apply $A = \pi r^2$ with $r = 5$: $A = \pi(5)^2 = 25\pi$.
$25\pi$. Apply $A = \pi r^2$ with $r = 5$: $A = \pi(5)^2 = 25\pi$.
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Find the circumference when $d = 10$ (leave the answer in terms of $\pi$).
Find the circumference when $d = 10$ (leave the answer in terms of $\pi$).
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$10\pi$. Apply $C = \pi d$ with $d = 10$: $C = \pi(10) = 10\pi$.
$10\pi$. Apply $C = \pi d$ with $d = 10$: $C = \pi(10) = 10\pi$.
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Find the circumference when $r = 6$ (leave the answer in terms of $\pi$).
Find the circumference when $r = 6$ (leave the answer in terms of $\pi$).
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$12\pi$. Apply $C = 2\pi r$ with $r = 6$: $C = 2\pi(6) = 12\pi$.
$12\pi$. Apply $C = 2\pi r$ with $r = 6$: $C = 2\pi(6) = 12\pi$.
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What is the approximate value of $\pi$ as a fraction that is often used for estimation?
What is the approximate value of $\pi$ as a fraction that is often used for estimation?
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$\pi \approx \frac{22}{7}$. Useful fraction approximation slightly larger than $\pi$.
$\pi \approx \frac{22}{7}$. Useful fraction approximation slightly larger than $\pi$.
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What is the approximate value of $\pi$ commonly used for mental math?
What is the approximate value of $\pi$ commonly used for mental math?
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$\pi \approx 3.14$. Common decimal approximation for calculations.
$\pi \approx 3.14$. Common decimal approximation for calculations.
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Identify the meaning of $\pi$ as a ratio involving circumference $C$ and diameter $d$.
Identify the meaning of $\pi$ as a ratio involving circumference $C$ and diameter $d$.
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$\pi = \frac{C}{d}$. $\pi$ is the constant ratio of circumference to diameter.
$\pi = \frac{C}{d}$. $\pi$ is the constant ratio of circumference to diameter.
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What is the relationship between radius $r$ and diameter $d$ in a circle?
What is the relationship between radius $r$ and diameter $d$ in a circle?
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$r = \frac{d}{2}$. Radius is half the diameter.
$r = \frac{d}{2}$. Radius is half the diameter.
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What is the relationship between diameter $d$ and radius $r$ in a circle?
What is the relationship between diameter $d$ and radius $r$ in a circle?
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$d = 2r$. Diameter is twice the radius.
$d = 2r$. Diameter is twice the radius.
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State the formula for the area of a circle in terms of radius $r$.
State the formula for the area of a circle in terms of radius $r$.
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$A = \pi r^2$. Area equals $\pi$ times the radius squared.
$A = \pi r^2$. Area equals $\pi$ times the radius squared.
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State the formula for the circumference of a circle in terms of diameter $d$.
State the formula for the circumference of a circle in terms of diameter $d$.
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$C = \pi d$. Circumference equals $\pi$ times the diameter.
$C = \pi d$. Circumference equals $\pi$ times the diameter.
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State the formula for the circumference of a circle in terms of radius $r$.
State the formula for the circumference of a circle in terms of radius $r$.
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$C = 2\pi r$. Circumference equals $2\pi$ times the radius.
$C = 2\pi r$. Circumference equals $2\pi$ times the radius.
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Find the diameter when the circumference is $C = 16\pi$.
Find the diameter when the circumference is $C = 16\pi$.
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$d = 16$. From $C = \pi d$: $16\pi = \pi d$, so $d = 16$.
$d = 16$. From $C = \pi d$: $16\pi = \pi d$, so $d = 16$.
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State the informal relationship between area $A$ and circumference $C$ using $A = \frac{1}{2}Cr$.
State the informal relationship between area $A$ and circumference $C$ using $A = \frac{1}{2}Cr$.
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$A = \frac{1}{2}Cr$. Shows area as half the product of circumference and radius.
$A = \frac{1}{2}Cr$. Shows area as half the product of circumference and radius.
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Identify the error: A student wrote $A = 2\pi r$ for the area. What is the correct formula?
Identify the error: A student wrote $A = 2\pi r$ for the area. What is the correct formula?
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$A = \pi r^2$. Student confused area with circumference formula.
$A = \pi r^2$. Student confused area with circumference formula.
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Identify the error: A student wrote $C = \pi r^2$ for circumference. What is the correct formula?
Identify the error: A student wrote $C = \pi r^2$ for circumference. What is the correct formula?
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$C = 2\pi r$. Student confused circumference with area formula.
$C = 2\pi r$. Student confused circumference with area formula.
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If the radius doubles from $r$ to $2r$, what happens to the area?
If the radius doubles from $r$ to $2r$, what happens to the area?
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It quadruples: $A\to 4A$. Since $A=\pi r^2$, doubling $r$ makes $A$ become $\pi(2r)^2=4\pi r^2$.
It quadruples: $A\to 4A$. Since $A=\pi r^2$, doubling $r$ makes $A$ become $\pi(2r)^2=4\pi r^2$.
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Find the circumference $C$ if the radius is $r=\frac{1}{2}$ (in terms of $\pi$).
Find the circumference $C$ if the radius is $r=\frac{1}{2}$ (in terms of $\pi$).
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$C=\pi$. Use $C=2\pi r$ with $r=\frac{1}{2}$: $C=2\pi(\frac{1}{2})=\pi$.
$C=\pi$. Use $C=2\pi r$ with $r=\frac{1}{2}$: $C=2\pi(\frac{1}{2})=\pi$.
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Identify the area formula written using diameter $d$ instead of radius $r$.
Identify the area formula written using diameter $d$ instead of radius $r$.
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$A=\pi\left(\frac{d}{2}\right)^2$. Substitute $r=\frac{d}{2}$ into $A=\pi r^2$.
$A=\pi\left(\frac{d}{2}\right)^2$. Substitute $r=\frac{d}{2}$ into $A=\pi r^2$.
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Find and correct the error: A student wrote $A=2\pi r^2$ for area.
Find and correct the error: A student wrote $A=2\pi r^2$ for area.
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Correct: $A=\pi r^2$. The 2 shouldn't multiply $r^2$ in the area formula.
Correct: $A=\pi r^2$. The 2 shouldn't multiply $r^2$ in the area formula.
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Find the radius $r$ if the area is $A=49\pi$.
Find the radius $r$ if the area is $A=49\pi$.
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$r=7$. From $A=\pi r^2$: $49\pi=\pi r^2$, so $r^2=49$ and $r=7$.
$r=7$. From $A=\pi r^2$: $49\pi=\pi r^2$, so $r^2=49$ and $r=7$.
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What is the relationship between diameter $d$ and radius $r$ in any circle?
What is the relationship between diameter $d$ and radius $r$ in any circle?
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$d=2r$. Diameter is twice the radius.
$d=2r$. Diameter is twice the radius.
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Find and correct the error: A student wrote $C=\pi r$ for circumference.
Find and correct the error: A student wrote $C=\pi r$ for circumference.
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Correct: $C=2\pi r$. Missing the factor of 2 in the circumference formula.
Correct: $C=2\pi r$. Missing the factor of 2 in the circumference formula.
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State the informal relationship between area and circumference using $A$ and $C$.
State the informal relationship between area and circumference using $A$ and $C$.
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$A=\frac{1}{2}Cr$. Area equals half the product of circumference and radius.
$A=\frac{1}{2}Cr$. Area equals half the product of circumference and radius.
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