All Common Core: High School - Geometry Resources
Example Questions
Example Question #11 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Calculate the arc length of a circle that has a central angle of degrees and a circumference of .
Refer to the following figure to help calculate the solution.
To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.
The algebraic formula for arc length is as follows.
where,
For this particular question the known information is,
Substitute these values into the formula and solve for the arc length.
Example Question #12 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Determine the area of the sector of a circle that has a central angle of degrees and a circumference of .
Refer to the following figure to help calculate the solution.
To calculate the area of the sector of the circle all that is needed is the central angle and the area of the circle. Since the central angle and circumference are given the area of the circle can be calculated.
The formulas to find the area and circumference of a circle are as follows.
The known information is,
Solving for the radius,
Now the area of the whole circle is,
Now, since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,
Example Question #15 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Calculate the arc length of a circle that has a central angle of degrees and a circumference of .
Refer to the following figure to help calculate the solution.
To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.
The algebraic formula for arc length is as follows.
where,
For this particular question the known information is,
Substitute these values into the formula and solve for the arc length.
Example Question #16 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Determine the area of the sector of a circle that has a central angle of degrees and a circumference of .
Refer to the following figure to help calculate the solution.
To calculate the area of the sector of the circle all that is needed is the central angle and the area of the circle. Since the central angle and circumference are given the area of the circle can be calculated.
The formulas to find the area and circumference of a circle are as follows.
The known information is,
Solving for the radius,
Now the area of the whole circle is,
Now, since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,
Example Question #17 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Calculate the arc length of a circle that has a central angle of degrees and an of .
Refer to the following figure to help calculate the solution.
To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.
The algebraic formula for arc length is as follows.
where,
For this particular question the known information is,
First, calculate the radius and the circumference.
Substitute these values into the formula and solve for the arc length.
Example Question #12 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Determine the area of the sector of a circle that has a central angle of degrees and an area of .
Refer to the following figure to help calculate the solution.
State the known information,
Since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,
Example Question #21 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Determine the area of the sector of a circle that has a central angle of degrees and an area of .
Refer to the following figure to help calculate the solution.
State the known information,
Since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,
Example Question #71 : Circles
Calculate the arc length of a circle that has a central angle of degrees and an of .
Refer to the following figure to help calculate the solution.
To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.
The algebraic formula for arc length is as follows.
where,
For this particular question the known information is,
First, calculate the radius and the circumference.
Substitute these values into the formula and solve for the arc length.
Example Question #23 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5
Calculate the arc length of a circle that has a central angle of degrees and an of .
Refer to the following figure to help calculate the solution.
To calculate the arc length of a circle that has a central angle of degrees and a circumference of , refer to the figure and the algebraic formula for arc length.
The algebraic formula for arc length is as follows.
where,
For this particular question the known information is,
First, calculate the radius and the circumference.
Substitute these values into the formula and solve for the arc length.
Example Question #71 : Circles
Determine the area of the sector of a circle that has a central angle of degrees and an area of .
Refer to the following figure to help calculate the solution.
State the known information,
Since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,