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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

Area for 10pts

What are the Surface Area formulas for a Sphere and Hemisphere?

Area for 10pts Answer

SASphere= 4πr2

SAHemisphere= 2πr2 + πr2

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

Density for 10pts

What is the formula for density?

Density for 10pts Answer

Volume

MassDensity

D

M

V D = VM

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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:

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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.

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return

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

Back to the Game Board!

Click here to return