Geometry
Name___________________________________ ID: 1
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Assignment
Date________________ Period____
Solve for x. Assume that lines which appear to be diameters are actual diameters. 1) 115°
x + 120
A) - 5 C) 3
B) 9 D) - 10
Find the measure of the arc or angle indicated. 2) C ?
E D 110 °
A) 40° C) 44°
B) 37° D) 55°
Find the missing side lengths. Leave your answers as radicals in simplest form. 3) x 60°
3
y
9 2 B) x = 6, y = 3 3 C) x = 3 3 , y = 6 D) x = 6 3 , y = 3 A) x = 6, y =
3
Worksheet by Kuta Software LLC
-1-
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Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. Leave your answers in terms of p for answers that contain p . 4)
2 km
A) 13.43p km³ C) 8.09p km³
B) 10.67p km³ D) 17.05p km³
Find the value of each trigonometric ratio. 5) sin X Y
6) cos C
12
Z
A
50
C 14
48
B 35
25 24 7 C) 25
37
A) X
35 37 35 C) 12
24 7 7 D) 24 B)
12 35 12 D) 37
A)
B)
7) tan Z 45
Z
X 27
36
Y
5 3 4 C) 5
3 4 3 D) 5
A)
B)
Find the missing side. Round to the nearest tenth. 8) 58°
x
12
A) 7.5 C) 19.2
B) 9.3 D) 9.4
Worksheet by Kuta Software LLC
-2-
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Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. 9) 4 3
x
A) 6 C) 4.7
B) 3 D) 5
Find the volume of each figure. Round your answers to the nearest whole, if necessary. 10)
11)
3 in
11 cm
10 in 8 in
10 cm 6 in
A) 72 in³ C) 80 in³
A) 183 cm³ C) 173 cm³
B) 69 in³ D) 44 in³
5 cm
B) 270 cm³ D) 550 cm³
Find the missing side lengths. Leave your answers as radicals in simplest form. 12)
13) 45°
x
y
30°
u
v
6
A) B) C) D)
x= x= x= x=
6 2, y = 2 12, y = 6 6, y = 12 6 2, y = 6
3
4
A) B) C) D)
u= u= u= u=
16, v = 4 3 8, v = 4 3 16, v = 8 3 8 3 , v = 16
Find the measure of the arc or angle indicated. 14) 90 °
X ?
W
61 °
G 54 ° V
A) 106° C) 99°
B) 101° D) 134° Worksheet by Kuta Software LLC
-3-
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15) 74 ° K
L ?
107 °
J Z
84 °
A) 76° C) 88°
B) 112° D) 78°
Decide whether the numbers can represesnt the side lengths of a triangle. If they can, classify if the three side lengths form an acute, obtuse, or right triangle. 16) 3 m, 12 m, 13 m A) Acute C) Not a Triangle
B) Obtuse D) Right
Use the information provided to write the equation of each circle. 17) Center: ( 2, - 14 ) Radius: 3 2
2
2
2
A) ( x - 2 ) + ( y + 14 ) = 9 B) ( x - 2 ) + ( y + 14 ) = 81 2
A) ( x + 13 )
2
C) ( x - 14 ) + ( y + 2 ) = 9 2
( )
21 , 13 2 Radius: 3
18) Center:
2
D) ( x - 2 ) + ( y + 14 ) = 1
( ) ( ) ( )
23 B) x 2 21 C) x 2 21 D) x 2
( )
21 + y+ 2
2
2
=3
2 2
+ ( y + 11 ) = 9 2 2
+ ( y - 13 ) = 3 2 2
+ ( y - 13 ) = 9
Find the volume of each figure. Round your answers to the nearest tenth, if necessary. 19)
11 yd
A) 999 yd³ C) 1693.3 yd³
7 yd
B) 2200.2 yd³ D) 1209.8 yd³ Worksheet by Kuta Software LLC
-4-
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Find the surface area of each figure. Round your answers to the nearest whole, if necessary. 20) 9 ft
5 ft
A) 440 ft² C) 587 ft²
B) 409 ft² D) 249 ft²
A box is represented below. How many cubic inches of sand can be placed in the box if we fill it half full. 21)
7 mi
10 mi
5 mi 5 mi 10 mi
A) 426 mi³ C) 350 mi³
B) 369 mi³ D) 356 mi³
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 22)
23)
10 in
6.3 in 9 in
4 in
A) 36.6 in² C) 52.2 in²
B) 129.4 in² D) 48.6 in²
8.7 in
A) 1038 in² C) 801 in²
B) 1062 in² D) 627 in²
Solve for x. Assume that lines which appear tangent are tangent. 24) 10 9 x 11
A) 10 C) 8
B) 5 D) 7
Worksheet by Kuta Software LLC
-5-
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Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 25)
9.3 in
A) 1086.9 in² C) 1160.9 in²
B) 856.3 in² D) 903.3 in²
State if the three side lengths form an acute, obtuse, or right triangle. 26) 7 mi, 26 mi, 72 mi A) Obtuse B) Right C) Acute Find the surface area of each figure. Round your answers to the nearest whole, if necessary. 27)
5 yd
A) 89 yd² C) 314 yd²
B) 51 yd² D) 79 yd²
Solve for x. Assume that lines which appear to be tangent are tangent. 28) 4x + 4
3 x + 15 30
A) 9 C) 11
B) 7 D) 0
Worksheet by Kuta Software LLC
-6-
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Use the information provided to write the equation of each circle. 29)
y 1 -2
-1
1
2
3
4
5
6 x
-1 -2 -3 -4 -5 -6 -7
2
2
2
2
2
2
2
2
A) ( x - 2 ) + ( y + 4 ) = 16 B) ( x - 2 ) + ( y + 4 ) = 4 C) ( x + 4 ) + ( y + 2 ) = 4 D) ( x - 3 ) + ( y + 3 ) = 4
Find the measure of the arc or angle indicated. 30)
W
64 ° Q
?
X
31) In Question #31, How is WXQ and WYQ related? A) They are both equal to 64° B) WXQ is larger than WYQ C) WYQ is larger than WXQ D) They are both equal to 32°
Y
A) 58° C) 48°
B) 65° D) 84°
Find the missing side lengths. Leave your answers as radicals in simplest form. 32) 8
60°
x
45°
A) 12 8 C) 3
B) 8
2
D) 8
3
Worksheet by Kuta Software LLC
-7-
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Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 33) 4.7 in
5 in
5 in
A) 69 in² C) 61 in²
B) 72 in² D) 36 in²
Find the volume of each figure. Round your answers to the nearest tenth, if necessary. 34)
11 yd 4 yd
A) 56.7 yd³ C) 64.5 yd³
B) 46.1 yd³ D) 184.3 yd³
Find the probability of each event. 35) A jar contains six black buttons and five brown buttons. If six buttons are picked at random, what is the probability that all of them are black? 1 » 1.515% 66 1 C) » 2.381% 42
1 » 0.216% 462 1 D) » 0.758% 132
A)
B)
36) Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle. 3, 5, 10. A) right B) acute C) obtuse D) Not a Triangle
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. 37)
38)
?
U
T S
N
M
45 ° V
?
70 ° L 125 °
G
A) 88° C) 31°
K
52 ° B
B) 61° D) 46°
Worksheet by Kuta Software LLC
-8-
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39) W hat is the definition of a tangent? A) A line that passes through a circle in two points. B) A line that passes through the center of a circle. C) A line that intersects a circle at one point. D) A line that touches the circle at two points but doesn't pass through. 40) W hat is the definition of faces? A) The polygons that solids are bounded by. B) A three deminsional figure. C) The point where three or more edges meet. D) A plane that passes through the widest part of a circle. 41) In a 45° - 45°-90° triangle, The _________ is 2 times as long as each leg A) Hypotenuse B) altitude C) short leg D) long leg
42) In a 30°-60°-90° tiangle, the _______ leg is 3 x/2 times as long as the hypotenuse. A) long B) opposite C) adjacent D) short
43) In a 30°-60°-90° triangle, the _____leg is half as long as the hypotenuse A) long B) adjacent C) short D) opposite 44) W hat is the definition of an edge? A) where 3 or more edges of a solid meet B) the polygons that solids are bounded by C) the intersectin of a spehere and a place D) a line segment formed by the intersection of two faces of a solid 45) The _______ of a circle is a chord that passes through the center of the circle. A) radius B) diameter C) tangent D) secant
Worksheet by Kuta Software LLC
-9-
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Geometry
Name___________________________________ ID: 1
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Assignment
Date________________ Period____
Solve for x. Assume that lines which appear to be diameters are actual diameters. 1) 115°
x + 120
* A) - 5 C) 3
B) 9 D) - 10
Find the measure of the arc or angle indicated. 2) C ?
E D 110 °
A) 40° C) 44°
B) 37° * D) 55°
Find the missing side lengths. Leave your answers as radicals in simplest form. 3) x 60°
3
y
9 2 *B) x = 6, y = 3 3 C) x = 3 3 , y = 6 D) x = 6 3 , y = 3 A) x = 6, y =
3
Worksheet by Kuta Software LLC
-1-
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Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. Leave your answers in terms of p for answers that contain p . 4)
2 km
A) 13.43p km³ C) 8.09p km³
* B) 10.67p km³ D) 17.05p km³
Find the value of each trigonometric ratio. 5) sin X Y
6) cos C
12
Z
A
50
C 14
48
B 35
25 24 7 * C) 25
37
A)
X
35 37 35 C) 12
24 7 7 D) 24 B)
12 35 12 * D) 37
A)
B)
7) tan Z 45
Z
X 27
36
Y
5 3 4 C) 5
3 4 3 D) 5
A)
* B)
Find the missing side. Round to the nearest tenth. 8) 58°
x
12
* A) 7.5 C) 19.2
B) 9.3 D) 9.4
Worksheet by Kuta Software LLC
-2-
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Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. 9) 4 3
x
A) 6 C) 4.7
B) 3 * D) 5
Find the volume of each figure. Round your answers to the nearest whole, if necessary. 10)
11)
3 in
11 cm
10 in 8 in
10 cm 6 in
* A) 72 in³ C) 80 in³
B) 69 in³ D) 44 in³
* A) 183 cm³ C) 173 cm³
5 cm
B) 270 cm³ D) 550 cm³
Find the missing side lengths. Leave your answers as radicals in simplest form. 12)
13) 45°
x
y
30°
u
v
6
A) B) C) *D)
x= x= x= x=
6 2, y = 2 12, y = 6 6, y = 12 6 2, y = 6
3
4
A) *B) C) D)
u= u= u= u=
16, v = 4 3 8, v = 4 3 16, v = 8 3 8 3 , v = 16
Find the measure of the arc or angle indicated. 14) 90 °
X ?
W
61 °
G 54 ° V
A) 106° C) 99°
* B) 101° D) 134° Worksheet by Kuta Software LLC
-3-
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15) 74 °
L
K
?
107 °
J Z
84 °
A) 76° C) 88°
B) 112° * D) 78°
Decide whether the numbers can represesnt the side lengths of a triangle. If they can, classify if the three side lengths form an acute, obtuse, or right triangle. 16) 3 m, 12 m, 13 m A) Acute C) Not a Triangle
* B) Obtuse D) Right
Use the information provided to write the equation of each circle. 17) Center: ( 2, - 14 ) Radius: 3 2
2
2
2
*A) ( x - 2 ) + ( y + 14 ) = 9 B) ( x - 2 ) + ( y + 14 ) = 81 2
A) ( x + 13 )
2
C) ( x - 14 ) + ( y + 2 ) = 9 2
2
D) ( x - 2 ) + ( y + 14 ) = 1
( )
21 , 13 2 Radius: 3
18) Center:
( ) ( ) ( )
23 B) x 2 21 *C) x 2 21 D) x 2
( )
21 + y+ 2
2
2
=3
2 2
+ ( y + 11 ) = 9 2 2
+ ( y - 13 ) = 3 2 2
+ ( y - 13 ) = 9
Find the volume of each figure. Round your answers to the nearest tenth, if necessary. 19)
11 yd
A) 999 yd³ * C) 1693.3 yd³
7 yd
B) 2200.2 yd³ D) 1209.8 yd³ Worksheet by Kuta Software LLC
-4-
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Find the surface area of each figure. Round your answers to the nearest whole, if necessary. 20) 9 ft
5 ft
* A) 440 ft² C) 587 ft²
B) 409 ft² D) 249 ft²
A box is represented below. How many cubic inches of sand can be placed in the box if we fill it half full. 21)
7 mi
10 mi
5 mi 5 mi 10 mi
A) 426 mi³ * C) 350 mi³
B) 369 mi³ D) 356 mi³
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 22)
23)
10 in
6.3 in 9 in
4 in
A) 36.6 in² * C) 52.2 in²
B) 129.4 in² D) 48.6 in²
8.7 in
A) 1038 in² C) 801 in²
* B) 1062 in² D) 627 in²
Solve for x. Assume that lines which appear tangent are tangent. 24) 10 9 x 11
A) 10 * C) 8
B) 5 D) 7
Worksheet by Kuta Software LLC
-5-
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Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 25)
9.3 in
* A) 1086.9 in² C) 1160.9 in²
B) 856.3 in² D) 903.3 in²
State if the three side lengths form an acute, obtuse, or right triangle. 26) 7 mi, 26 mi, 72 mi A) Obtuse B) Right * C) Acute Find the surface area of each figure. Round your answers to the nearest whole, if necessary. 27)
5 yd
A) 89 yd² C) 314 yd²
B) 51 yd² * D) 79 yd²
Solve for x. Assume that lines which appear to be tangent are tangent. 28) 4x + 4
3 x + 15 30
A) 9 * C) 11
B) 7 D) 0
Worksheet by Kuta Software LLC
-6-
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Use the information provided to write the equation of each circle. 29)
y 1 -2
-1
1
2
3
4
5
6 x
-1 -2 -3 -4 -5 -6 -7
2
2
2
2
2
2
2
2
A) ( x - 2 ) + ( y + 4 ) = 16 *B) ( x - 2 ) + ( y + 4 ) = 4 C) ( x + 4 ) + ( y + 2 ) = 4 D) ( x - 3 ) + ( y + 3 ) = 4
Find the measure of the arc or angle indicated. 30)
W
64 ° Q
?
X
31) In Question #31, How is WXQ and WYQ related? A) They are both equal to 64° B) WXQ is larger than WYQ C) WYQ is larger than WXQ *D) They are both equal to 32°
Y
* A) 58° C) 48°
B) 65° D) 84°
Find the missing side lengths. Leave your answers as radicals in simplest form. 32) 8
60°
x
45°
A) 12 8 C) 3
* B) 8
2
D) 8
3
Worksheet by Kuta Software LLC
-7-
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Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 33) 4.7 in
5 in
5 in
A) 69 in² C) 61 in²
* B) 72 in² D) 36 in²
Find the volume of each figure. Round your answers to the nearest tenth, if necessary. 34)
11 yd 4 yd
A) 56.7 yd³ C) 64.5 yd³
* B) 46.1 yd³ D) 184.3 yd³
Find the probability of each event. 35) A jar contains six black buttons and five brown buttons. If six buttons are picked at random, what is the probability that all of them are black? 1 » 1.515% 66 1 C) » 2.381% 42
1 » 0.216% 462 1 D) » 0.758% 132
A)
* B)
36) Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle. 3, 5, 10. A) right B) acute C) obtuse * D) Not a Triangle
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. 37)
38)
?
U
T S
N
M
45 ° V
?
70 ° L 125 °
G
A) 88° C) 31°
40°
K
52 ° B
* B) 61° D) 46°
Worksheet by Kuta Software LLC
-8-
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39) W hat is the definition of a tangent? A) A line that passes through a circle in two points. B) A line that passes through the center of a circle. *C) A line that intersects a circle at one point. D) A line that touches the circle at two points but doesn't pass through. 40) W hat is the definition of faces? *A) The polygons that solids are bounded by. B) A three deminsional figure. C) The point where three or more edges meet. D) A plane that passes through the widest part of a circle. 41) In a 45° - 45°-90° triangle, The _________ is 2 times as long as each leg * A) Hypotenuse B) altitude C) short leg D) long leg
42) In a 30°-60°-90° tiangle, the _______ leg is 3 x/2 times as long as the hypotenuse. * A) long B) opposite C) adjacent D) short
43) In a 30°-60°-90° triangle, the _____leg is half as long as the hypotenuse A) long B) adjacent * C) short D) opposite 44) W hat is the definition of an edge? A) where 3 or more edges of a solid meet B) the polygons that solids are bounded by C) the intersectin of a spehere and a place *D) a line segment formed by the intersection of two faces of a solid 45) The _______ of a circle is a chord that passes through the center of the circle. A) radius * B) diameter C) tangent D) secant
Worksheet by Kuta Software LLC
-9-
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