Name ______________________
Geometry – Semester 2
SHOW ALL OF YOUR WORK. Remember which formulas you will be given.
1) Cone Country Ice Cream Shoppe has mini cones with a diameter of 4 cm and a height of 4
cm. Cone country wanted to make a bigger cone that will hold 2.5 times more ice cream.
The diameter will stay the same. Find the height of the large cone.
a)
b)
c)
d)
7.5 cm
10.0 cm
12.6 cm
31.4 cm
2) Write the standard equation of the circle if the center is (-3, 4) and a point on the circle is
the origin.
a) (x + 3)2 + (y – 4)2 = 5
b) (x - 3)2 + (y + 4)2 = 5
c) (x + 3)2 + (y – 4)2 = 25
d) (x - 3)2 + (y + 4)2 = 25
3) Find the total surface area of the right prism.
4
7
a)
b)
c)
d)
92 3 units2
84  8 3 units2
28 3 units2
84  4 3 units2
4) Determine the total surface area of the right circular cone.
6
a)
b)
c)
d)
24 2 units2
36 2 units2
9  + 18 2 units2
18  + 18 2 units2
5) Find the diameter of the given cylinder if the volume is 288  units3.
8
a)
b)
c)
d)
6 units
12 units
18 units
36 units
6) In circle C with radius 3 units, find the length of the intercepted arc of
a)
b)
c)
d)
C if m C  120 .
2 units
3 units
4 units
9 units
7) A wooden door stop has the dimensions as shown. If the volume of the door stop is 72
units3, find x.
x
6
a)
b)
c)
d)
4
3 units
6 units
9 units
Cannot be determined
8) A cylindrical glass soap dish is made by cutting a hemisphere out of a cylinder. How much
glass is needed to create the dish? The measurements of the soap dish are on the diagram
as below, listed in inches.
10

6
7
a)
b)
c)
d)
9)
108 
556 
844 
988 
inches3
inches3
inches3
inches3
A cylindrical glass (with diameter 10 cm) is full of water and then poured into the
rectangular pan. Approximately what is the maximum height of the cylinder so that the
box will not overflow?
??
10 cm
12 cm
10 cm
a)
b)
c)
d)
12.2 cm
30.6 cm
61.1 cm
120.6 cm
8 cm
10) Write the equation of a circle given the following:
b) center (2, 3), point on circle (8, -5)
a) center (5, -6), radius 15 .
c) center at origin, passing through (6, 8)
11) Find the length of one side of the regular polygon shown in simplified radical form.
12) Find the slant height of the regular
square pyramid when height is 15.
16
13) Find the height of the following cone
given the slant height is 15 units and the
diameter is 20 units.
14) Find the total surface area of the right
triangular prism.
10
12
12
15) Find the total surface area of the right
circular cone. Round to nearest tenth.
16) Find the volume of a sphere with an 8
inch diameter. Leave your answer in
terms of  .
6
12
17) In a right square pyramid, the area of the base is 100ft2 and the height of the prism is 12 ft.
Find the slant height.
18) Find the volume of a right cone if the base has a diameter of 12 and a height of 10. Keep
your answer in terms of .
19) In a regular square pyramid whose base edges measure 8 inches. If the altitude of the
pyramid is 8 inches, find the slant height as a simplified radical.
20) You need to paint a child’s toy that is made up of a cylinder and hemisphere, as shown
below. The radius of the cylinder is 14 cm and its altitude measures 30 cm. A small paint
can covers 2000 cm2.
a) What is the surface area of the child’s toy? (Keep in terms of .)
30 cm
14 cm
b) How many cans are needed to paint the surface if it requires two coats?
21) If the solid below is a cylinder with a cone cut out of it, find its volume in terms of .
3 cm
10 cm
22) Use the figure below to answer the following questions.
a) Identify a radius
A
b) Identify a diameter
H
c) Identify a chord
C
d) Identify a central angle
e) Identify a tangent
62°
31°
15.5°
124°
F
D
23) Given m  B = 31°, Find m  A. A
a)
b)
c)
d)
G
B
B
31°
C
D
E
24) Find the area of the shaded region and the arc length to the nearest tenth.
72
7 cm
25) Your geometry teacher and their geometry teacher friends decided to have dessert after
their pizza party and now are moving onto a cookie cake. If only 70.7 in2 of cookie cake
is left and the central angle of the uneaten portion was 100o, find the radius of the cookie
cake to the nearest tenth.
26)Find the values of x and y.
x°
2y
°
100°
87°
27)Find the measure of angle ACB.