Unit 8: Area & Volume Review

Circles & Polygons

100

Find the area of sector GCH below. Round to two decimal places and include units. 

`A = \theta/360\times\pir^2`

`A = 75/360\times\pi(5)^2`

`A = 16.36 cm^2`

200

Find the area of the regular dodecagon (12 sides) below. The length of each side is 9 inches. 

`tan(15)=4.5/a`

`a=4.5/tan(15)=16.79`

`A_t=1/2(9)(16.79)=75.57`

`A_d=75.57\times12=906.89` sq.in.``

300

Find the radius of the circle below given the central angle and arc length of the major (larger) arc LM.

`AL = \theta/360\times2pir`

`38.95=260/360\times2pir`

`38.95=4.538r`

`r=8.58 cm`

400

Find the area of a regular icosagon (20 sides) with a perimeter of 160 feet. 

``Each side`= 160/20=8` ft``

``Each triangle`=360/20=18^o`

`tan(9) = 4/a`

`a = 4/tan(9) = 25.255`

`A_T = 1/2(8)(25.255) = 101.02`

`A_I = 101.02\times 20 = 2020.4 ft^2`

Volume

100

Find the volume of the oblique triangular prism below. 

`V=Bh`

`V=(1/2\times7\times10)(5)`

`V=175 ` cubic inches``

200

Find the height of the cylinder below. 

`V=pir^2h`

`4608pi=pi(12)^2h`

`4608=144h`

`h=32 ` inches``

300

Find the volume of the sphere below. 

`C=2pir`

`7pi=2pir`

`7=2r`

`r=3.5`

`V=4/3pir^3`

`V=4/3pi(3.5)^3`

`V=179.59` cubic inches``

400

Find the volume of the square-based pyramid below. 

`h^2+2.5^2=8^2`

`h=7.6`

`V=1/3Bh`

`V=1/3(5^2)(7.6)`

`V=63.33 cm^3`

Surface Area

100

Find the surface area of the square-based pyramid below. 

`SA=(5)^2 + 4(1/2\times5\times8)`

`SA=25+4(20)`

`SA=105 cm^2`

200

Find the surface area of this hemisphere. Leave your answer in terms of pi. 

`SA=1/2(4pir^2)+pir^2`

`SA=2pi(6)^2+pi(6)^2`

`SA=72pi+36pi=108pi` sq. in.``

300

The cone below has a volume of 216π in³. Find the surface area. 

`V=1/3pir^2h`

`216pi=1/3pir^2(18)`

`216=6r^2`

`36=r^2 ` so ` r=6`

`6^2+18^2=l^2`

`l=18.97`

`SA=pir^2+pirl`

`SA=pi(6)^2+pi(6)(18.97)`

`SA=470.74` sq. in.``

400

Find the surface area of the green solid shown below. Round to two decimal places. 

`SA=2(`sector`)+2(`flat side`)+` curved side``

`A_S=78/360\timespi(4)^2`

`A_S=10.89`

`A_[FS]=4\times 10=40`

``Arc`=78/360\times2pi(4)`

``Arc`=5.445`

`A_[CS]=5.445\times 10 = 54.45`

`SA=2(10.89)+2(40)+54.45`

`SA= 156.24 m^2`

Composite Shapes

100

Find the volume of the solid below. Round to two decimal places.  

`V=2(1/3Bh)`

`V=2(1/3(8^2)(5))`

`V=213.33 cm^3`

200

Find the volume of the composite shape below. 

`V_(Cyl)=1/2(pir^2h)`

`V_(Cyl)=1/2(pi(2)^24)`

`V_(Cyl)=25.13`

`V_(Cu)=Bh=(4^2)(4)=64`

`V=64+25.13`

`V=89.13` cubic inches``

300

*DAILY DOUBLE*

Find the surface area of the composite solid below. Round to two decimal places. 

`SA_[Co]=pirl`

`SA_[Co]=pi(3)(3\sqrt(2))`

`SA_[Co]=39.99 cm^2`

`SA_[Cyl]=pir^2+2pirh`

`SA_[Cyl]=pi(3)^2+2pi(3)(7)`

`SA_[Cyl]=160.22 cm^2`

`SA = 200.21 cm^2`

400

Find the volume of the shape below.

 

`V_C=Bh=(12^2)12=1728`

``Pyramid base side length``

`s=6\sqrt(2) ` (isosceles)``

`V_P=1/3Bh`

`V_P=1/3(6\sqrt(2))^2(12)`

`V_P=288`

`V=1728-288=1440` cubic inches``

500

***FINAL JEOPARDY***

Find the surface area of the hexagonal pyramid below. 

`L^2=sqrt(3)^2+3^2`

`L=3.46`

`A_H=1/2(2)(\sqrt(3))\times 6`

`A_H=10.39`

`A_T=(1/2)(2)(3.46)\times 6`

`A_T=20.78`

`SA=10.39+20.78=31.18` sq. in.``