Date post: | 20-Jan-2016 |
Category: |
Documents |
Upload: | alban-sharp |
View: | 222 times |
Download: | 0 times |
Surface Area and Volume Answers to CH. 11 Exam
Find the volume
β’ To find the volume, first figure out the shapes involved
π ππππ+π ππ¦ππππππ+π h hππππ π πππ
Find the volume
π ππππ+π ππ¦ππππππ+π h hππππ π πππ
13π π2h+ππ 2h+
23ππ 3
13π 52β5+π 52 β5+
23π 53
1253
π+125π+2503
π
250πβ785.4
Find the surface area
Figure out the parts of the shapes involved then add them together.
πΏ . π΄ .ππππ+πΏ . π΄ .ππ¦ππππππ+πΏ . π΄ .h hππππ π πππ
Find the surface area
πΏ . π΄ .ππππ+πΏ . π΄ .ππ¦ππππππ+πΏ . π΄ .h hππππ π πππ
πππ+2π hπ +2ππ 2βπ β5 ββ50+2 βπ β5 β5+2 βπ β52
25β2π+50π+50π25β2π+100πβ 425.23
To find surface area, you do not include the circles, just the outside of the composite shape.
Find the volume
To find the volume, form break the composite figure into three prisms and add together
Find the volume
π πππππ+ππππππ’π+π π ππππ
12
44
9
3
4
43
5
(12 β4 β 4)+(9 β3 β 4)+(5 β3 β 4)192+108+60π½=πππ
Find the surface area
To find the surface area of the figure you have to break the composite figure into rectangles and add their areas together
Find the surface area
back
4
12
bottom
4
10
front
45
4
3
side
4 3 3
129
5
top
44
3
3
ΒΏ (12 β4 )+ΒΏ(12 β4 )+ (9 β3 )+(5 β3 )+ΒΏ(5 β4 )+(4 β4 )+(4 β3 )+ΒΏ(10 β4 )+ΒΏ(4 β4 )+(3 β3 )+(3 β3)ΒΏππ+π (ππ)+ππ+ππ+ππΒΏπππ
Find the volume
To find the volume of the figure you have to break apart the composite figure
Find the volume
Half cylinder with radius 3.5
Rectangular prism
ΒΏ12π ππ¦ππππππ 1+
12πππ¦ππππππ 2+π ππππ π
ΒΏ12
(π hπ )+ 12
(π hπ )+( hππ€ )
ΒΏ12
(π 3.5β8 )+ 12
(π 3.5 β4 )+(8 β4 β7)
βπππ .π
Find the surface area
To find the surface area of the figure you have to break apart the composite figure
Find the surface area
Half cylinder with radius 3.5
Rectangular prism without the top or the side
ΒΏ12π .π΄ .ππ¦ππππππ 1+
12π .π΄ .ππ¦ππππππ 2+π . π΄ .ππππ π
ΒΏ12
(2π β3.5 β8 )+2π 3.52+ 12
(2π β3.5 β4 )+2π 3.52+2 (8 β 4 )+(4 β7 )+(8 β7)
ΒΏ12
(2π hπ +2π π2 )+ 12
(2π hπ +2π π2 )+2 ( ππ€ πππππ‘ )+(ππ€π πππ )+ (ππ€πππ‘π‘ππ )
βπππ .ππ
Use algebra to express volume
To solve algebraically, first identify the shapes and the dimensions given.
Use algebra to express volumeWhat we know.
πππππ’π =2πh hπππ π‘=πΒΏ13π ΒΏ
ΒΏ 4 π2ππ3
ΒΏ πππππ π
The volume of the solid is 360 cubic feet. Find the value of .
First use the Pythagorean Theorem to find the missing side of the triangle
π2+π2=π2
π2+64=289ππππ π πππ π πππ=15
Now solve for π ππππ π= hπ΅360=
12β15 β8β π₯
360=60 π₯π=π
Find the volume
Find the volume of the solid of revolution rotated about the line.
Find the volume of the solid of revolution rotated about the line.
π=π πππππβπ π ππππ
π=π π2hβππ 2hπ=π β42 β4βπ β22 β4π=64πβ16ππ½=ππ π π½ βπππ .π
Find the total surface area of the solid of revolution found by rotating the triangle about the vertical line
What does the solid look like?
15
8
Now that we know what the solid looks like, we realize that the surface area is what is covered by the green.
What is the surface area covered by green?
π . π΄ .=π΄πππππππππ+πΏ .π΄ .ππ¦ππππππ+πΏ . π΄ .ππππΒΏππ 2+2π hπ +πππΒΏπ β152+2π β15 β8+π β15 β17ΒΏ225π+240π+255πΒΏππππ ΒΏππππ .ππ
π=15h=8π=15
Solid I is similar to Solid II, find the value of .
First find the ratio of the solids.
or
ππ
=π₯β22π₯+3
Set up your proportion and solve
2 π₯+3=3π₯β6π=π
What is the height of a cone whose slant height is twice the radius and whose volume is
π
h2πh2+π2=(2π )2
h2+π2=4π 2
π=βππβ
first find h
Plug in and solve
π=13ππ2h=343π β3
2413π π2π β3=343πβ3
24
ππ3β33
=343π β324π=
ππππ3
3=343π β3
24 β3π3
3=343π24π
π3=3 β34324
π3=3438
1
8
h=π β3π=
ππ
βπ
Bathman just discovered that the valve on his cement truck (why he has a cement truck I donβt know), failed during the night and that all the contents ran out to form a giant cone of hardened cement. To make an insurance claim, Bathman needs to figure out how much cement is in the cone. The circumference of its base is 44 feet and it is 5 feet high. Calculate the volume.
Use circumference to find
C=2 Ο π4 4=2Ο ππππ
=π βπ
Now that you have r, plug in an solve
π ππππ=13Ο π2h
π ππππ=13Ο β72 β5
π½ ππππ=ππππ
πβπππ
The solid below is a peg with a square hole. Find its surface area.
In order to find the surface area we will have to:
Find the lateral area of the cylinder
Find the area of the circle minus the square for the top and bottom
Find the lateral area of the square peg
In order to find the surface area we will have to:
Find the lateral area of the cylinder
πΏ . π΄ .ππ¦ππππππ=2π hππΏ . π΄ .ππ¦ππππππ=2 βπ β7 β13πΏ . π΄ .ππ¦ππππππ=2 βπ β7 β13π³ . π¨ .ππππππ ππ=ππππ
Next, we will have to:
Find the area of the circle minus the square for the top and bottom
π΄π‘ππ /πππ‘π‘ππ=π΄ππππππβπ΄π ππ’πππΒΏ2(ππ2βπ 2)ΒΏ2(π β72β42)β2(138)βπππ
Next we will have to:
Find the lateral area of the square peg
πΏ . π΄ .πππ= hππΏ . π΄ .πππ= (4 β 4 )13
π³ . π¨ .πππ=πππ
Now we put them all together
+
πΏ . π΄ .ππ¦ππππππ=2π hπ
π΄π‘ππ /πππ‘π‘ππ=π΄ππππππβπ΄π ππ’πππ
πΏ . π΄ .πππ= hπ+
ππππ +ΒΏπππ+ΒΏππππΊ . π¨ . βππππ .π
Find the lateral area
β’ A water bottle in the shape of a cylinder has a volume of 500 cubic centimeters. The diameter of a base is 7.5 cm. What is the approximate height of the bottle?
β’ Andrew is working on a car and has a funnel with the dimensions shown. He uses the funnel to put oil in his car. Oil flows out of the funnel at a rate of 45 milliliters per second. How long will it take to empty the funnel when it is full of oil?
Find the volume
Find the volume