Jeopardy Review Game Volume, Density and Surface Area of a Sphere.
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Transcript of Jeopardy Review Game Volume, Density and Surface Area of a Sphere.
Jeopardy Review Game
Volume, Density and Surface Area of a Sphere
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.
Participation:
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
Note to Teacher:
Volume Area Densit
yOh My!
Grab Bag
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?
Prisms/Cylinders:V=BH
Pyramids/Cones:V= BH
B=Area of BaseH=Height of Solid
Volume for 10ptsAnswer
3
1
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Volume for 20pts
Find the volume
60 ft
20 ft40 ft
V= (40)(20)(60)V= 48,000ft3
Volume for 20ptsAnswer
60 ft
20 ft40 ft
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Volume for 30pts
Find the volume (in terms of pi)
24 in
18 in
V=BH(1/2)V=(πr2)(H)(1/2)
Volume for 30ptsAnswer
24 in
18 in
r = 9inV= (92π)24(1/2)V= (81π)12V = 972 π in3
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Volume for 40pts
Find the volume of the regular octagonal pyramid.
a = 9 cms = 15cm
32 cm
V= BH
Volume for 40ptsAnswer
32 cm
n = 8a = 9 cms = 15cm
3
1
35760
3
)32(5403
322
)15)(9)(8(
32
cm
Hnas
V
V
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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 50ptsAnswer
12 in
r
r
rC
C
24
248
2
48
3
2
2
2304
4)576(3
12)24(
3
)(
inV
V
V
HrV
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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?
8 m
12 m
6 m
4 m
Area for 20pts Answer
The base is a trapezoid
8 m
12 m
6 m
4 m
2
21
28
2)14(2
4)86(2
)(
mA
A
A
hbbA
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Area for 30pts
Find the exact surface area of this sphere
cm4
5
Area for 30pts Answer
SASphere= 4πr2
cm4
5
2
2
25.6
4
25
16
254
4
54
cmSA
SA
SA
SA
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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=12πmr =6m
2
2
72
362
62
cmSA
SA
SA
r
r
rC
C
6
212
2
12
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Area for 50pts
Find the exact surface area of the solid
3in 5in
7in
Area for 50pts Answer
70
752
A
A
3in 5in
7in
Outside Edge: r =5
Inside Edge: r =3
Top/Bottom:A= πr2
42
732
A
A
16
16
925
3)(r 9
5)(r 25
bottom
top
top
sml
big
A
A
A
A
A
Total:
2in 14416164270
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Density for 10pts
What is the formula for density?
Density for 10pts Answer
Volume
MassDensity
D
M
V D = VM
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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 20ptsAnswer
3/ 2.0
90
18
cmgD
D
D = V
M
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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 Answer
3/ 3.11
9.9
4.351
cmgD
D
3
2
9.9
)1.1)(3(
cmV
V
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Density for 40pts
Find the density of the submerged object (round to the nearest hundredth)
4.3cm
5cm
Density for 40pts Answer
4.3cm
5cm
3/ 52.0
875.26
44
cmgD
D
3
2
875.26
)3.4(25.6
)3.4)(5.2(
cmV
V
V
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Density for 50pts
A ball causes the water in the container to rise as indicated.
Approximate the height of displaced water
(to the nearest hundredth)
7cm7cm
3cm
x
Density for 50pts Answer
7cm7cm
3cm
x
36
)27(3
4
33
4 3
V
V
V
3
3
4rVsphere
331.2
3649
49
)7)(7(
cmx
x
xV
xV
Sphere: Displacement:
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Oh My! for 10pts
Find the exact volume of the cone
12mm
5mm
Oh My! for 10pts Answer
3
2
2
100
4)25(3
12)5(
3
)(
mmV
V
V
HrV
12mm
5mm
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Oh My! for 20pts
Find the volume of this trapezoidal prism
6 m
10 m
4 m
3 m
Oh My! for 20pts Answer
6 m
10 m
4 m
3 m
3
21
150
)10)(3)(5(
102
3)10(
102
3)64(
2
)(
mV
V
V
V
Hhbb
V
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Oh My! for 30pts
The volume of a right triangular prism is 270ft3 . Find x
9 ft10 ft
x
Oh My! for 30pts Answer
9 ft10 ft
x
x
x
x
x
Hbh
V
6
45270
59270
102
9270
2X = 6ft
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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 cm and the base is 6cm. What is the approximate height of the pyramid? (nearest hundredth)
33
Oh My! for 40pts Answer
?
6
3√3 H
H
H
H
Hbh
V
188.46
33240
6
318240
3
1
2
)33(6240
3
1
2H ≈ 46.19cm
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Oh My! for 50ptsWater 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
150
3
2
24.982,753
000,240
)150(40
ftV
V
V
$𝟓𝟎 ,𝟐𝟔𝟓 .𝟒𝟖
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Grab Bag for 10pts
Describe how we use displacement in math.
Grab Bag for 10pts AnswerIt 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
350
27
1350
yds
33 127
13
ydft
ydft
3ft
3ft
3ft1yd
1yd
1yd
= 1yd327ft3
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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
7
49
1964
196
2
2
r
r
r
SA
3
3
3
76.1436
3
1372
)343(3
4
73
43
4
cmV
V
V
V
rV
cm7
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Grab Bag for 40pts
Find the approximate volume of the solid (nearest hundredth)
5in
7in
3in
2in
Grab Bag for 40pts Answer
5in
7in
3in
2in
3105
)7)(5)(3(
inV
Vprism
3
3
76.16
3
16
)8(3
2
23
2
inV
V
V
Vhemi
376.121
76.16105
inV
Vtotal
About 121.76i
n3
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Grab Bag for 50ptsThis 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.
4in
5in(Round to the
nearest thousandth)
Grab Bag for 50pts Answer
4in
5in
6
4
2
1
3
4
3
3
rV
rV
725.326
5.626
)625.15(46
)5.2(4 3
V
V
V
V
Outer: Inner:
755.166
326
)8(46
)2(4 3
V
V
V
V
Total:
3
3
97.15755.16725.32
970.156
5.30
6
32
6
5.62
in
in
15.97in3
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