Math 1010

Measurement and Geometry Unit

Test 3 Review

Dimensional Analysis for 10 points:

How many minutes is a student in class one semester if the student takes 12 credit hours? (Assume each class is one hour and 1 semester = 14 weeks.)

$\frac{12\;credit\;hours}{\;1\;week}\times\frac{14\;weeks}{\;semester}\times\frac{60\;mins}{1\;hour}$

10,080 minutes

Dimensional Analysis for 20 points:

How many cubic feet of dirt fit in a crate with a volume of 14,400 cubic inches?

$\frac{14,400\;in^3}{\;1\;crate}\times\frac{1^3\;ft^3}{\;12^{3\;}in^3}=8.3 \;cubic \;feet$

Dimensional Analysis for 30 points:

A sprinter runs 100 meters in 11 seconds. What is the sprinter’s speed in mph?

$\frac{100\;m}{11\;sec}\times\frac{60\;sec}{1\;min}\times\frac{60\;min}{1\;hr}\times\frac{1\;km}{1000\;m}\times\frac{1\;mile}{1.61\;km}=20.33\; mph$

Perimeter and Area for 10 points:

How much fencing is needed to enclose the park?

The yard is sahped by attaching a large ractangle on top of a smaller rectangle. The top rectangle has a length of 100 yards and a width of 40 yards. The bottom rectangle that is joined to the lower right side of the upper rectangle has a length of 60 yards and a width of 80 yards.

$100+120+60+80+40+40=440\; yards$

Perimeter and Area for 20 points:

How many square miles are included in the state park shown?

The state park isin the shape of a triangle. the base of the triangle is 10000 feet. The height of the triangle is 6500 feet.

$A=\frac12bh$

$A=\frac12(10,000)(6500)=32,500,000\;ft^2$

$\frac{32,500,000\;ft^2}{triangle}\times\frac{1^2\;mile^2}{5280^2\;ft^2}=1.17 \;square\; miles$

Perimeter and Area for 30 points:

Find the area of the shaded region inside the track:

The track is in the shape of a rectangle with a half circle attached to each end of the rectangle. The length of the rectangle is 80 meters. The width of the rectangle is 40 meters. The diameter of the circle is 40 meters, the same as the width of the rectangle.

Area of the rectangle: $A=lw=40(80)=3200\;m^2$

Area of the circle: $A=\pi r^2=\pi(20^2)=1256.64\; m^2$

Area of half the circle is $628.32 \;m^2$

$3200+628.32=3828.32\;m^2$

Surface Area and Volume for 10 points:

Find the amount of cardboard used to make a cereal box 30 cm tall, 20 cm wide, and 3 cm deep. (Assume no overlapping edges.)

$SA=2lw+2lh+2wh$

$SA=2(30)(20)+2(30)(3)+2(20)(3)$

$SA=1200+180+120$

SA=1500 square cm

Surface Area and Volume for 20 points:

What is the volume of a Pepsi can 4.8 inches tall with a diameter of 2.6 inches?

$V=\pi r^2h$

$V=\pi(1.3)^2(4.8)$

V=25.48 cubic inches

Surface Area and Volume for 30 points:

How many pounds would a king size feather pillow weigh if it were stuffed to a height of 6 inches? The dimensions of a king size pillow are 20 by 36 inches. Feathers weigh 0.02 grams per cubic cm.

$V=lwh$

$V=(20)(36)(6)=4320\;in^3$

$\frac{4320\;in^3}{pillow}\times\frac{2.54^3\;cm^3}{1^3\;in^3}\times\frac{0.02\;g}{1\;cm^3}\times\frac{1\;kg}{1000\;g}\times\frac{2.2\;lbs}{1\;kg}=3.11\; pounds$

More Practice for Exam 3

A family pool holds 10,000 gallons of water. How many cubic meters is this?

$\frac{10,000\;gal}{pool}\times\frac{1\;ft^3}{7.48\;gal}\times\frac{1^3\;yd^3}{3^3\;ft^3}\times\frac{1^3\;m^3}{1.09^3\;yds^3}=38.23\; m^3$

The average American high school student is in class 330 minutes/day.
1. How many hours per day is this?
  $\frac{330\;min}{1\;day}\times\frac{1\;hr}{60\;min}=5.5 \;hours$
2. How many seconds per day is this?
  $\frac{330\;min}{1\;day}\times\frac{60\;sec}{1\;min}=19,800\; seconds$
Sixty mph is how many ft/sec?

$\frac{60\;miles}{1\;hour}\times\frac{1\;hour}{60\;min}\times\frac{1\;min}{60\;sec}\times\frac{5280\;ft}{1\;mile}=88 \;feet\; per\; second$

If a person weighs 125 lbs, 8 oz., how many milligrams do they weigh?

$\frac{128.5\;lbs}{\;person}\times\frac{1\;kg}{2.2\;lbs}\times\frac{1000\;g}{1\;kg}\times\frac{1000\;mg}{1\;g}=57,045,454.55\; mg$

A small herd of cattle consumes fourteen bales of hay in two weeks. How many bales will this herd consume in a year?

$\frac{14\;bales}{2\;weeks\;}\times\frac{52\;weeks}{1\;year}=364\; bales\; per\; year$

During the previous year, Zach's weather station measured 0.8 yards of rain. Express this amount in cm.

$\frac{0.8\;yds}{1\;year\;}\times\frac{1\;m}{1.09\;yd}\times\frac{100\;cm}{1\;m}=73.39\; cm/yr$

Saffron costs $368.00 per ounce. Determine how many grams you can purchase for $15.00.

$\frac{1\;oz}{\$368\;}\times\frac{1\;lb}{16\;oz}\times\frac{\;1\;kg}{2.2\;lbs}\times\frac{1000\;g}{1\;kg}\times\frac{\$15}{}=1.16\; grams$

A gas station is charging $1.299 per gallon of gas. What would be the price for a liter of gas?

$\frac{\$1.2999}{1\;gal}\times\frac{0.2642\;gal}{1\;L}=$0.34 \;per \;liter$

A car consumes 25.00 gallons of fuel when driving a distance of 400.0 km. How many gallons will it consume when driving 250.0 miles?

$\frac{25\;gals}{400\;km}\times\frac{1.61\;km}{1\;mile}\times\frac{250\;miles}{}=25.16 \;gallons$

A standard piece of notebook paper measures 8.5 inches by 11 inches. How many square centimeters is this?

$A=lw$

$A=(8.5)(11)=93.5\;in^2$

$\frac{93.5\;in^2}{paper}\times\frac{2.54^2\;cm^2}{1^2\;in^2}=603.22\;cm^2$

A water balloon is in the shape of a sphere with a diameter of 6 inches.
1. What is it’s volume in cubic feet?
  $V=\frac43 \pi r^3$
  
  $V=\frac43 \pi (3)^3$
  
  $V=113.1\;in^3$
  
  $\frac{113.1\;in^3}{ballon}\times\frac{1^3\;ft^3}{12^3\;in^3}=0.065\;ft^3$
2. How many cups of water will it hold?
Find the area of the shaded area.

The shaded area is a figure formed by a semicircle at the bottom with right triangles attached to the left and to the right of the circle at the top. The bases of the triangles form the diameter of the semicircle. the triangles are identical in size and their bases meet halfway across the diameter of the circle. The radius of the circle is 4 feet and the height of both triangles is 9 feet.

Area of a Triangle: $A=\frac12 bh$

$A=\frac12 (4)(9)=18\;ft^2$

Area of 2 triangles: $18\times2=36\;ft^2$

Area of a Circle: $A=\pi r^2$

$A=\pi (4)^2=50.27\;ft^2$

Area of half the circle: $50.27/2=25.13\; ft^2$

Area of the shaded region: $36+25.13=61.13\;ft^2$

Find the are of the shaded area.

The shaded area is a triangle with a rectangle cut out of the bottom part of it. Th height of the triangle is 8 meters and the base of the triangle is 8 meters. The length of the rectangle is 6 meters and the width of the rectangle is 2 meters.

Area of a Triangle: $A=\frac12 bh$

$A=\frac12 (8)(8)=32\;m^2$

Area of a Rectangle: $A=lw$

$A=(2)(6)=12\;m^2$

Area of the shaded region: $32-12=20\;m^2$

You have some leftover soup in a can. The can has a radius of 5 cm and a height of 10 cm. How much plastic wrap will you need in square centimeters to completely cover the can?

Surface Area of a Cylinder: $SA=2\pi r^2 +2\pi rh$

$SA=2\pi (5)^2 +2\pi (5)(10)=471.24\;cm^2$

A company is deciding which box to use for their merchandise. The first box measures 8 inches by 6.25 inches by 10.5 inches. The second box measures 9 inches by 5.5 inches by 11.75 inches. Which box requires more material to make?

Surface Area of a Rectangular Prism: $SA=2lw+2lh+2wh$

The surface area of the first box: $SA=2(8)(6.25)+2(8)(10.5)+2(6.25)(10.25) =399.25\;in^2$

The surface area of the second box: $SA=2(9)(5.5)+2(9)(11.75)+2(5.5)(11.75) =439.75\;in^2$

The second box requires more material.

Which box in question #15 holds more merchandise?

Volume of a Rectangular Prism: $V=lwh$

The volume of the first box: $V=(8)(6.25)(10.5) =525\;in^3$

The volume of the second box: $V=(9)(5.5(11.75)=581.625\;in^3$

The second box holds more.