Jeopardy Review Game
Volume, Density and Surface Area of a
Sphere
Participation:
Everyone should have their own
piece of paper to write down
each question. Show all work on
your paper, they will be collected
at the end of class and counted
as a participation grade for today.
Note to Teacher:
If at any time you need to return to
the game board click the “I <3
Math” picture
Pictures on the slides following the
answers will also return you to the
game board
Density Oh My!
Grab
Bag
Volume
Area
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
50
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Volume for 10pts
What are the volume formulas for
prisms/cylinders and
pyramids/cones?
Volume for 10pts
Prisms/Cylinders:
V=BH
Pyramids/Cones:
1
V= 3 BH
B=Area of Base
H=Height of Solid
Answer
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Volume for 20pts
Find the volume
60 ft
20 ft
40 ft
Volume for 20pts
Answer
V= (40)(20)(60)
V= 48,000ft3
60 ft
20 ft
40 ft
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Volume for 30pts
Find the volume (in terms of pi)
18 in
24 in
Volume for 30pts
Answer
V=BH(1/2)
r = 9in
V=(πr2)(H)(1/2) V= (92π)24(1/2)
V= (81π)12
V = 972 π in3
18 in
24 in
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Volume for 40pts
Find the volume of the regular
octagonal pyramid.
a = 9 cm
s = 15cm
32 cm
Volume for 40pts
1
V= 3 BH V
 nas 

H
2 

V
3
 (8)( 9)(15) 

 32
2



3
540( 32)

3
 5760cm 3
Answer
n=8
a = 9 cm
s = 15cm
32 cm
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Volume for 50pts
Find the exact volume of the cone if
the circumference of the base is
48πin
12 in
Volume for 50pts
C  48
C  2r
48  2r
24  r
Answer
(r 2 ) H
V
3
2
( 24 )12
V
3
V  (576 )4
V  2304 in
3
12 in
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Area for 10pts
What are the Surface Area
formulas for a Sphere and
Hemisphere?
Area for 10pts Answer
SASphere= 4πr2
SAHemisphere= 2πr2 + πr2
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Area for 20pts
What is the area of the base of
this solid?
8m
12 m
4m
6m
Area for 20pts Answer
The base is a trapezoid
(b1  b2 )h
A
2
(6  8)4
A
2
A  (14)2
A  28m
2
8m
12 m
4m
6m
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Area for 30pts
Find the exact surface area of this
sphere
5
cm
4
Area for 30pts Answer
SASphere= 4πr2
2
 5
SA  4  
 4
 25 
SA  4  
 16 
25
SA  
4
SA  6.25 cm 2
5
cm
4
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Area for 40pts
An igloo (hemisphere) has an
outside circumference of 12πm.
What is the exact surface area of
the igloo’s outside?
Area for 40pts Answer
C  12
C  2r
12  2r
SA  2 6
SA  2 36
6r
SA  72 cm
2
2
C=12πm
r =6m
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Area for 50pts
Find the exact surface area of the
solid
3in
5in
7in
Area for 50pts Answer
Outside Edge:
r =5
A  2 57
A  70
Inside Edge:
r =3
A  2 37
A  42
Top/Bottom: A= πr2
Abig  25
(r  5)
Asml  9
(r  3)
Atop  25  9
Atop  16
Abottom  16
3in
5in
Total:
70  42  16  16  144 in
2
7in
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Density for 10pts
What is the formula for density?
Density for 10pts
Answer
Mass
Density 
Volume
M
D
V
M
D=
V
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Density for 20pts
If a rock has a mass of 18 grams
and displaces 90cm3 of water.
What is its density?
Density for 20pts
Answer
18
M
D
D=
90
V
3
D  0.2 g / cm
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Density for 30pts
A piece of metal weighs 351.4 grams
and causes the water level in a
cylindrical container (r = 3cm) to
rise 1.1cm. What is the density of the
piece of metal?
(Round to the nearest tenth)
Density for 30pts
V  ( 3 )(1.1)
2
V  9.9cm
3
351.4
D
9.9
3
D  11.3 g / cm
Answer
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Density for 40pts
Find the density of the submerged
object (round to the nearest hundredth)
5cm
4.3cm
Density for 40pts
Answer
V  ( 2.5 )( 4.3)
V  6.25 (4.3)
2
V  26.875cm
44
D
26.875
3
D  0.52 g / cm
3
5cm
4.3cm
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Density for 50pts
A ball causes the water in the
container to rise as indicated.
Approximate the
height of displaced
x
water
3cm
7cm
7cm
(to the nearest hundredth)
Density for 50pts
Vsphere
4 3
 r
3
Sphere:
Displacement:
4 3
V  3
3
4
V  ( 27 )
3
V  36
x
3cm
7cm
7cm
Answer
V  (7 )( 7 ) x
V  49 x
49 x  36
x  2.31cm 3
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Oh My! for 10pts
Find the exact volume of the cone
5mm
12mm
Oh My! for 10pts
Answer
(r ) H
V
3
2
( 5 )12
V
3
V  ( 25 )4
2
5mm
12mm
V  100 mm
3
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Oh My! for 20pts
Find the volume of this trapezoidal
prism
6m
10 m
3m
4m
Oh My! for 20pts
 (b1  b2 )h 
V 
H
2


 ( 4  6 )3 
V 
10
2 

 (10)3 
V 
10
 2 
V  (5)( 3)(10)
V  150m
3
Answer
6m
10 m
3m
4m
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Oh My! for 30pts
The volume of a right triangular
prism is 270ft3 . Find x
10 ft
x
Oh My! for 30pts
X = 6ft
10 ft
x
Answer
 bh 
V   H
 2
 9x 
270   10
 2 
270  9 x 5
270  45 x
6x
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Oh My! for 40pts
The volume of a pyramid with an
isosceles triangular base is
240cm3. The height of the triangle
is 3 3 cm and the base is 6cm.
What is the approximate height
of the pyramid? (nearest
hundredth)
Oh My! for 40pts
H ≈ 46.19cm
?
3√3
6
Answer
 bh   1 
V 
H  
 2  3
 6(3 3 )   1 
H  
240  
 3
2


 18 3 
H
240  

6




240  3 3 H
46.188  H
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Oh My! for 50pts
Water world has a cylindrical water
tower that is 150ft tall and has a
diameter of 80ft. If they charge
$0.50 per gallon, how much money
could they make from selling all the
water in this tank? Round to the
nearest whole dollar.
(1 cubic foot = 7.5 gallons)
Oh My! for 50pts
Answer
40
V  40  (150)
2
V  240,000
V  753,982.24 ft
150
3
753,982.2369
= 100,530.9649𝑔𝑎𝑙
7.5
100,530.9679 0.50 = $50,265.48
$𝟓𝟎, 𝟐𝟔𝟓. 𝟒𝟖
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Grab Bag for 10pts
Describe how we use
displacement in math.
Grab Bag for 10pts Answer
It helps us find the volume of
irregularly shaped objects. The
volume of the displaced water is
equal to the volume of the
submerged object.
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Grab Bag for 20pts
If the foundation of a structure has
a volume of 1350ft3 how many
cubic yards of concrete did it
take to make the foundation?
(3 feet = 1yard)
Grab Bag for 20pts Answer
3 ft  1yd
27 ft  1yd
3
3ft
=
27ft3
3ft
3ft
3
1yd
1yd3
1yd
1yd
1350
27
3
50 yds
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Grab Bag for 30pts
If the surface area of a sphere is
196 π cm2, find its volume to the
nearest hundredth.
Grab Bag for 30pts Answer
SA  196
4r  196
V
2
r  49
r7
2
V
V
7cm
V
V
4 3
 r
3
4
3
 7
3
4
 ( 343)
3
1372


3
3
 1436.76cm
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Grab Bag for 40pts
Find the approximate volume of
the solid (nearest hundredth)
2in
3in
5in
7in
Grab Bag for 40pts Answer
About
121.76in3
3in
5in
7in
2 3
V prism  ( 3)( 5)( 7) Vhemi   2
3
V  105in3
2
V  (8)
3
2in
16
V 
3
3
V  16.76in
Vtotal  105  16.76
V  121.76in3
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Grab Bag for 50pts
This toy part is made of plastic. The
outer-hemisphere diameter is 5in
and the inner-hemisphere diameter
is 4in. Find the volume of the plastic.
5in
4in
(Round to the
nearest thousandth)
Grab Bag for 50pts Answer
4r 3  1  Outer:
Inner:
3
V 
3
 
4

(
2
)
3  2  V  4 ( 2.5)
V 
6
6
3
4r
4(8)
V 
4(15.625)
V 
V 
6
6
6
32
62
.
5
3
15.97in
V 

V 

6
6
V  16.755
V  32.725
5in
4in
Total: 62.5
32
30.5


 15.970in3
6
6
6
32.725  16.755  15.97in3
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