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Tenth Grade (Grade 10) Circles Questions

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Grade 10 Circles CCSS: HSG-MG.A.2

A typical hard drive disk platter (where the information of a hard drive is stored) is a circular disk. The portion on which information can be stored is an annulus (a disk with a circular hole in the center). The diameter of a typical platter is 3.5 in., and the diameter of the hole is 1.2 in. The platter can store information on both sides of the disk. If the density of the disk is approximately

$58.9 \ "MB"//"in."^2$ , how much data can the disk store, to the nearest MB?

5 MB
500 MB
1000 MB
2000 MB

Grade 10 Circles

Given the equation of a circle

$(x - 5)^2 + (y + 1)^2 = 9$ , what is the sum of the x-coordinate of the center, the y-coordinate of the center, and the radius of the circle?

13
7
5
-1

Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

If we are to translate circle B to circle A, which of the following translations would accomplish this?

Translate circle B by $vec{AB}$ .
Translate circle B by $vec{BA}$ .
Translate circle B by its radius.
Translate circle B by the radius of circle A.

Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

Which of the following is the best definition for similar figures?

Figures which are similar in area and perimeter.
Figures having congruent sides and angles.
One shape can be mapped to another through a sequence of rotations, translations, reflections, and/or dilation.
One shape can be mapped to another through rigid transformations.

Grade 10 Circles

If the measure of arc ED is 120° and the measure of angle BAC is 44°, what is the measure of arc BC?

34°
48°
32°
64°

Grade 10 Circles CCSS: HSG-MG.A.2

A factory had a chemical spill that released a dangerous substance into the air. Right around the factory, in a half mile radius, the concentration is about 40 ppm. The concentration of the chemical decreases by about 4 ppm every half mile further away one is from the factory. It can be assumed that the substance dispersed evenly in all directions. The population density in the area where the factory is located is about 150 people per square mile. If less than 12 ppm concentration of the substance is considered safe for people, how many people need to be evacuated from the area around the factory (rounded to the nearest person)?

414 people
3,600 people
5,773 people
7,540 people

Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

In order to compare the two circles (circle A and B), we would need to translate one onto the other. What part of the circle should we focus on in order to make this comparison?

Center
Radius
Circumference
Chord

Grade 10 Circles

Given

$C/(C')=0.25$ and

$r'=2$ find

$r$ . Use the formulas

$C/(C')=r/(r')=d/(d')$ or

$A/(A')=d^2/(d'^2)=r^2/(r'^2)$ (where

$C, r, d, A$ represent the circumference, radius, diameter, and area of a circle).

$r'=0.125$
$r'=2.25$
$r'=1.75$
$r'=0.5$

Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

Is the work and are conclusions from parts B through G enough to prove that any two circles are similar? If not, why?

Yes, they are enough.
No, we need to consider the case where we move circle A instead of circle B.
No, we need set up a two-column table.
No, we need to consider more sizes of circles first.

Grade 10 Circles

A circle of radius r = 3 centered at the origin (0,0) will intersect the line y = 3 at how many points?

1
5
2
Infinite many

Grade 10 Circles

A compass allows us to draw a .

ray
straight line
radius
circle

Grade 10 Circles

Given

$C/(C')=2.5$ and

$r=3$ find

$r'$ . Use the formulas

$C/(C')=r/(r')=d/(d')$ or

$A/(A')=d^2/(d'^2)=r^2/(r'^2)$ (where

$C, r, d, A$ represent the circumference, radius, diameter, and area of a circle).

$r'=1.2$
$r'=7.5$
$r'=5.5$
$r'=0.5$

Grade 10 Circles

Josh's lawn service company offers services within a 20 mile radius of his office. When the service area is represented graphically with the office located at (0, 0), what is the equation that represents the service area?

$x^2 +y^2=20$
$x^2+y^2=40$
$x^2+y^2=400$
$x^2+y^2=4000$

Grade 10 Circles

Given

$A'=1.8$ ,

$A=0.64$ , and

$r'=0.75$ find

$r$ . Use the formulas

$C/(C')=r/(r')=d/(d')$ or

$A/(A')=d^2/(d' ^2)=r^2/(r' ^2)$ (where

$C, r, d, A$ represent the circumference, radius, diameter, and area of a circle).

$r=.64$
$r=.86$
$r=.45$
$r=.25$

Grade 10 Circles CCSS: HSG-C.A.2

Which is true for intersecting chords?

One chord is half of the other chord.
Their difference is -1.
The product of their divided lengths are equal.

Grade 10 Circles

Given

$A'=7.1$ ,

$r=4.5$ , and

$r'=1.5$ find

$A$ . Use the formulas

$C/(C')=r/(r')=d/(d')$ or

$A/(A')=d^2/(d' ^2)=r^2/(r' ^2)$ (where

$C, r, d, A$ represent the circumference, radius, diameter, and area of a circle).

$A=9$
$A=27$
$A=64$
$A=2.2$

Grade 10 Circles

Given

$d'=4$ ,

$r=3$ , and

$r'=2$ find

$d$ . Use the formulas

$C/(C')=r/(r')=d/(d')$ or

$A/(A')=d^2/(d'^2)=r^2/(r'^2)$ (where

$C, r, d, A$ represent the circumference, radius, diameter, and area of a circle).

$d=0.17$
$d=9$
$d=6$
$d=2.7$

Grade 10 Circles

This question is a part of a group with common instructions. View group »

What is the missing reason in step 3?

Measure of central angle is 1/2 the measure of intercepted arc
Intersecting Secant Theorem
Sum of the angles in a triangle is half of the sum of the non-overlapping central angles in a circle
Measure of inscribed angle is 1/2 the measure of intercepted arc

Grade 10 Circles

This question is a part of a group with common instructions. View group »

What is the missing reason in step 5?

Triangle ABD looks like a right triangle
Tangent lines intersect all lines at a right angle
A tangent line is perpendicular to the diameter
The Pythagorean Theorem

Grade 10 Circles

This question is a part of a group with common instructions. View group »

What is the missing reason in step 5?

Multiplicative Identity Property
Multiplicative Inverse Property
Multiplicative Property of Equality
Closure Property of Multiplication

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Tenth Grade (Grade 10) Circles Questions