All Common Core: 7th Grade Math Resources
Example Questions
Example Question #191 : Plane Geometry
The area of a circle is . Give the circumference of the circle in terms of
.
Let .
The area of a circle can be calculated as , where
is the radius of the circle.
The circumference can be calculated as , where
is the radius of the circle.
Example Question #1 : Circumference Of A Circle
The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius inches; the width of the rectangle is
inches. What is the length of the rectangle?
inches
inches
inches
inches
inches
inches
The circumference of a circle with radius inches is
inches.
The perimeter of the rectangle is therefore inches. To find its length, substitute
and
into the equation and solve for
:
inches
Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4
A manufacturer makes wooden circles out of square blocks of wood. If the wood costs $0.25 per square inch, what is the minimum waste cost possible for cutting a circle with a radius of 44 in.?
5808 dollars
1936π dollars
1936 dollars
7744 – 1936π dollars
1936 – 484π dollars
1936 – 484π dollars
The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 88 inches for our problem. Its total area would be 88 * 88 or 7744 in2.
Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2 or π * 442 = 1936π in2. Therefore, the area remaining would be 7744 – 1936π. The cost of the waste would be 0.25 * (7744 – 1936π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 4 from our subtraction. This would give us: 0.25 * 4 * (1936 – 484π). Since 0.25 is equal to 1/4, 0.25 * 4 = 1. Therefore, our final answer is: 1936 – 484π dollars.
Example Question #21 : Geometry
A manufacturer makes wooden circles out of square blocks of wood. If the wood costs $0.20 per square inch, what is the minimum waste cost possible for cutting a circle with a radius of 25 in.?
500 - 125π dollars
500 dollars
2500 - 625π dollars
625 - 25π dollars
625 dollars
500 - 125π dollars
The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 50 inches for our problem. Its total area would be 50 * 50 or 2500 in2.
Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2 or π * 252 = 625π in2. Therefore, the area remaining would be 2500 - 625π. The cost of the waste would be 0.2 * (2500 – 625π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 5 from our subtraction. This would give us: 0.2 * 5 * (500 – 125π). Since 0.2 is equal to 1/5, 0.2 * 625 = 125. Therefore, our final answer is: 500 – 125π dollars.
Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4
What is the circumference of the circle provided?
In order to solve this problem, we need to recall the formula for the circumference of a circle:
or
The circle in this question provides us with the radius, so we can use the first formula to solve:
Solve:
Example Question #1 : Area Of A Circle
What is the area of a circle that has a diameter of inches?
The formula for finding the area of a circle is . In this formula,
represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by
.
Now we use for
in our equation.
Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4
What is the area of a circle with a diameter equal to 6?
First, solve for radius:
Then, solve for area:
Example Question #1 : Radius
The diameter of a circle is . Give the area of the circle.
The area of a circle can be calculated using the formula:
,
where is the diameter of the circle, and
is approximately
.
Example Question #4 : Area Of A Circle
The diameter of a circle is . Give the area of the circle in terms of
.
The area of a circle can be calculated using the formula:
,
where is the diameter of the circle and
is approximately
.
Example Question #5 : Area Of A Circle
The radius of a circle is . Give the area of the circle.
The area of a circle can be calculated as , where
is the radius of the circle, and
is approximately
.
All Common Core: 7th Grade Math Resources
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