Honors Geometry 9. Homework Answers for Section 12.4 Find the volume and the total surface area of the prism shown.
V = BH
10
=
13
=
( )
1
2
1
2
bh ( 10)
( 24) ( 5) ( 10) = 600 u3
( )
24
1
AT.S. = 2
2
bh
+ 2bh + bh
= ( 24) ( 5) + 2( 13) ( 10) + ( 24) ( 10) = 620 u2
10a. Find the volume and the total surface area of the right cylindrical solid shown.
V = BH
12
= ( π r 2 ) ( H)
=
9
81
4
π ( 12) = 243π u3
AT.S. = 2( π r2) + 2π rH
=
162
4
π + 9π ( 12) =
297π
2
u2
10b. Find the volume and the total surface area of the right cylindrical solid shown.
V = BH
=
6
6
=
20
[
1
2
1
2
]
( π r2) ( H)
( 36π ) ( 20) = 360π u3
AT.S. = 2
( )
1
2
π r2
+
1
2
( 2π rH) + bh
= 36π + 120π + 240 = ( 156π + 240) u2
Baroody Page 1 of 5 Honors Geometry 11. Homework Answers for Section 12.4 When Hilda computed the volume and the surface area of a cube , both answers had the same
numerical value. Find the length of one side of the cube.
V = AT.S.
x
⇒ BH = 6s2
⇒ x 3 = 6x 2
x
⇒x=6u
x
12. Find the volume and the surface area of the regular hexagonal right prism .
V = BH
=
10
[ ( )]
6
s2 3
4
( H)
= [6(9 3 )]( 10) = 540 3 u3
[ ( )]
AT.S. = 2 6
6
s2 3
4
+ 6( bh)
= 108 3 + 6( 6) ( 10) = (108 3 + 360) u2
13. Find the volume of a cube in which a face diagonal is 10.
V = BH
10
= [(5 2 )(5 2 )](5 2 )
5 2
= 250 2 u3
5 2
5 2
Baroody Page 2 of 5 Honors Geometry 15. Homework Answers for Section 12.4 A rectangular container is to be formed by folding the cardboard along the dotted lines. Find the
volume of this container.
7
7
9
10
3
V = BH
= [( 9) ( 3) ]( 7) = 189 u3
9
16. The cylindrical glass is full of water, which is poured into the rectangular pan. Will the pan
overflow? If yes, by how much? All measurements are in cm.
15
5
15
10
8
V = BH
V = BH
= ( π r2 ) H
= ( bh) H
= ( 16π ) ( 15) = 240π ≈ 753.98 cm 3
= ( 15) ( 10) ( 5) = 750 cm 3
∴ it will overflow by about 4 cc's
Baroody Page 3 of 5 Honors Geometry 17. Homework Answers for Section 12.4 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole
unit, what is
a. The total volume it contains?
b. The total area of the sheet metal needed to manufacture it?
a. V = V Half Cylinder + V Prism
3
3
8 in
=
=
( )
1
2
1
2
π r2 H + ( bh) H
( 9π ) ( 10) + ( 6) ( 8) ( 10) = ( 45π + 480)
6 in
10 in
≈ 621 in3
(
b. AT.S. = 2( 6 ⋅ 8) + 2( 8 ⋅ 10) + ( 6) ( 10) + 2
1
2
( 9π )
)
+ ( 3π ) ( 10)
= 96 + 160 + 60 + 39π = 316 + 39π ≈ 439 in2
18. A cistern is to be built of cement. The walls and bottom will be 1 ft. thick. The outer height will be
20 ft. The inner diameter will be 10 ft. To the nearest cubic foot, how much cement will be
needed for the job?
V = V Outer Cylinder - V Inner Cylinder
= ( π R2) H - ( π r2) H
10
20
= ( 36π ) ( 20) - ( 25π ) ( 19)
= 720π - 475π = 245π ≈ 770 ft3
1
1
Baroody 1
Page 4 of 5 Honors Geometry 19. Homework Answers for Section 12.4 A wedge of cheese is cut from a cylindrical block. Find the volume and the total surface area of
this wedge.
V=
40°
15
=
20
40
360
1
9
(V Cylinder)
( 400π ) ( 15) =
(
2000π
3
)
u3
AT.S. = ATop & Bottom + ACylindrical Side + ARectangular Sides
[
=2
40°
=
=
1
9
( 400π )
800π
9
(
+
]
+
1
9
[2π ( 20) ( 15) ] + 2( 20) ( 15)
600π
+ 600
9
1400π
+ 600
9
)
u2
Top View
20. An ice cube manufacturer makes ice cubes with holes in them. Each cube is 4
cm on a side and the hole is 2 cm in diameter.
2
a. To the nearest tenth, what is the volume of ice in each cube?
b. To the nearest tenth, what will be the volume of the water left when
ten cubes melt? (Water's voume decrease by 11% when it changes
from a solid to a liquid.)
4
c. To the nearest tenth, what is the total surface area (including the
inside of the hole) of a single cube?
d. The manufacturer claims that these cubes cool a drink twice as fast
as regular cubes of the same size. Verify whether this claim is true
by a comparision of surface areas. (Hint: The ratio of areas is equal
to the ratio of cooling speeds.)
4
4
a. V = VPrism - VCylinder = (bh)H - ("r2)H = [(16) - "](4) = (64 - 4") ! 51.4 cm3
b. VWater = 10[VIce Cube](.89) = 514(.89) ! 457.8 cm3
c. AT.S. = AT.S. of Prism - 2(ACircle) + AL.S. of Inside Cylinder = 6(16) - 2" + 2"(4) = 96 + 6" ! 114.8 cm2
AT.S. of New Cube
d.
Baroody AT.S. of Old Cube
=
114.8
1.2
!
, so the claim is untrue!
96
1
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