Name : ______________________________________________
Geometry A U8D4 Applications Using Conversions
Warm Up
1. What is the area of the rectangle below whose side
lengths measure 3 units by 5 units?
3. Use the following picture to explain why
15
12
Date: __________________________
3
5
4
3
2. What is the area of the × rectangle below?
1
is the same as 1 .
4
4. Figures 1 and 2 below show two polygonal regions used to approximate the area of the region inside a parabola and above the 𝑥axis.
a.
Use the shaded polygonal region in Figure 1 to give a lower estimate of the area 𝑎 under the curve and above the 𝑥-axis.
b.
Use the shaded polygonal region to give an upper estimate of the area 𝑎 under the curve and above the 𝑥-axis.
c.
Use (a) and (b) to give an average estimate of the area 𝑎.
1.
2.
A rectangle with dimensions 21.6 × 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the rectangle.
a.
Find the area of the shaded region.
b.
Explain how you determined the area of the shaded region.
Two triangles △ 𝐴𝐵𝐶 and △ 𝐷𝐸𝐹 are shown below. The two triangles overlap forming △ 𝐷𝐺𝐶.
a.
The base of figure 𝐴𝐵𝐺𝐸𝐹 is comprised of segments of the following lengths: 𝐴𝐷 = 4, 𝐷𝐶 = 3, and 𝐶𝐹 = 2. Calculate the
area of the figure 𝐴𝐵𝐺𝐸𝐹.
b.
Explain how you determined the area of the figure.
In the following triangular pyramid, a plane passes through the pyramid so that it is parallel to the base and results in the crosssection △ 𝐴′𝐵′𝐶′. The altitude from 𝑉 is drawn; the intersection of the altitude with the base is 𝑋, and the intersection of the
altitude with the cross-section is 𝑋′. If the distance from 𝑋 to 𝑉 is 18 mm, the distance from 𝑋′ to 𝑉 is 12 mm, and the area of
△ 𝐴′𝐵′𝐶′ is 28 mm2 , what is the area of △ 𝐴𝐵𝐶?
Name : ______________________________________________
Date: __________________________
Geometry A U8D4 Applications Using Conversions
1) Change 12 lbs. into ounces. 12 oz. 48 oz. 96 oz. 192 oz.
2) Change 8 lbs. into ounces.
9) Change 312 oz. into pounds and ounces.
17 lb. 18 lb. 5 oz. 19 lb. 8 oz. 20 lb.
oz. 4 oz. 128 oz. 32 oz.
3) Change 15 lbs. 5 oz. into ounces
245 oz. 30 oz. 10 oz. 240 oz.
10) Change 4
4) Change
lbs. into ounces. 76 oz. 72 oz. 66 oz. 60 oz.
lb. into ounces. 16 oz. 12 oz. 9 oz. 8 oz.
11) Change
oz.
lbs. into ounces. 96 oz. 98 oz. 100 oz. 122
5) Change 2 qt. into ounces. 128 oz. 96 oz. 64 oz. 32 oz.
6) Change 52 oz. into pounds and ounces.
3 lb. 6 oz. 3 lb. 8 oz. 32 oz. 3 lb. 4 oz.
12) Change
lbs. into ounces.
136 oz. 144 oz. 152 oz. 160 oz.
7) Change 220 oz. into pounds and ounces.
13 lbs. 12 oz. 12 lbs. 10 oz. 10 lbs. 12 oz. 16 lbs. 10 oz.
13) Convert 6 pts. to qt. 3 qts. 4 qts.
8) Change 70 oz. into pounds and ounces.
2 lbs. 6 oz. 3 lbs. 1 oz. 3 lbs. 3 oz. 4 lbs. 6 oz.
qts. 6 qts.
14) Convert
c. to oz. 6 oz. 4 oz. 3 oz. 2 oz.
15) Convert 4 qt. to pts16 pts. 8 pts. 4 pts. 2 pts.
1.
oz.
1 lb.
Water
Dry milk solids
Sugar, granulated
Yeast, compressed
Flour, bread
Salt
Shortening, vegetable
17) Convert
c. to oz. 4 oz. 2 oz. 1 oz. 3 oz.
1 lbs.
=
2c.
1 oz.
=
1 lb.
1 oz.
1 lb.
1 oz.
1 lb.
=
=
=
=
=
c.
2c.
3T.
4c.
2T.
2c.
Use the recipe for soft rolls below. Convert the weight of the 16 oz. of dry milk solids to an equivalent volume measure using the
weight/volume information.
Soft Rolls
Weight/Volume Information
9 lbs.
16 oz.
1 lb.
8 oz.
14 lbs.
oz.
1 lb.
3.
qt. to c. 12 c. 8 c. 4 c. 3 c.
Use the recipe for soft rolls below. Convert the weight of the 9 lbs. of water to an equivalent volume measure using the
weight/volume information.
Soft Rolls
Weight/Volume Information
9 lbs.
16 oz.
1 lb.
8 oz.
14 lbs.
2.
16) Convert
Water
Dry milk solids
Sugar, granulated
Yeast, compressed
Flour, bread
Salt
Shortening, vegetable
1 lbs. = 2c.
1 oz. =
1 lb.
1 oz.
1 lb.
1 oz.
1 lb.
=
=
=
=
=
c.
2c.
3T.
4c.
2T.
2c.
Use the recipe for soft rolls. Convert the weight of the 1 lb. of granulated sugar to an equivalent volume measure using the
weight/volume information.
Soft Rolls
Weight/Volume Information
9 lbs.
16 oz.
1 lb.
8 oz.
14 lbs.
oz.
1 lb.
Water
Dry milk solids
Sugar, granulated
Yeast, compressed
Flour, bread
Salt
Shortening, vegetable
1 lbs. = 2c.
1 oz. =
1 lb.
1 oz.
1 lb.
1 oz.
1 lb.
=
=
=
=
=
c.
2c.
3T.
4c.
2T.
2c.
4.
Use the recipe for soft rolls. Convert the weight of the 14 lbs. of bread flour to an equivalent volume measure using the
weight/volume information.
Soft Rolls
Weight/Volume Information
9 lbs.
16 oz.
1 lb.
8 oz.
14 lbs.
oz.
1 lb.
5.
1 lb.
1 oz. =
1 lb.
1 oz.
1 lb.
1 oz.
1 lb.
=
=
=
=
=
c.
2c.
3T.
4c.
2T.
2c.
Water
Dry milk solids
Sugar, granulated
Yeast, compressed
Flour, bread
Salt
Shortening, vegetable
1 lbs. = 2c.
1 oz. =
1 lb.
1 oz.
1 lb.
1 oz.
1 lb.
=
=
=
=
=
c.
2c.
3T.
4c.
2T.
2c.
Use the recipe for polenta. Convert the volume of the 2 qts. of water to an equivalent weight measure using the weight/volume
information.
Polenta
Weight/Volume Information
2 qts.
2 t.
4 c.
Water
Salt
Cornmeal
2 lbs. = 1 qt.
1 oz. = 8t.
1 lb. = 4c.
Use the recipe for polenta. Convert the volume of the 2 t. of salt to an equivalent weight measure using the weight/volume
information.
Polenta
Weight/Volume Information
2 qts.
2 t.
4 c.
8.
1 lbs. = 2c.
Use the recipe for soft rolls. Convert the weight of the 4½ oz. of salt to an equivalent volume measure using the weight/volume
information.
Soft Rolls
Weight/Volume Information
oz.
7.
Salt
Shortening, vegetable
9 lbs.
16 oz.
1 lb.
8 oz.
14 lbs.
6.
Water
Dry milk solids
Sugar, granulated
Yeast, compressed
Flour, bread
Water
Salt
Cornmeal
2 lbs. = 1 qt.
1 oz. = 8t.
1 lb. = 4c.
Use the recipe for basic pie dough. Convert the volume of the 3 c. of pastry flour to an equivalent weight measure using the
weight/volume information.
Basic Pie Dough
Weight/Volume Information
3 c.
1 c.
2 t.
1 c.
c.
Flour, pastry
Shortening, vegetable
Salt
Water, ice-cold
16 oz.
16 oz.
1 oz.
8 oz.
=
=
=
=
Dry mild solids
1 oz. =
4 c.
2 c.
8 t.
2 c.
c.
9.
Use the recipe for basic pie dough. Convert the volume of the 1 c. of vegetable shortening to an equivalent weight measure
using the weight/volume information.
Basic Pie Dough
Weight/Volume Information
3 c.
1 c.
2 t.
1 c.
c.
10.
16 oz.
16 oz.
1 oz.
8 oz.
=
=
=
=
Dry mild solids
1 oz. =
4 c.
2 c.
8 t.
2 c.
c.
Use the recipe for basic pie dough. Convert the volume of the 2 t. of salt to an equivalent weight measure using the
weight/volume information.
Basic Pie Dough
Weight/Volume Information
3 c.
1 c.
2 t.
1 c.
c.
11.
Flour, pastry
Shortening, vegetable
Salt
Water, ice-cold
Flour, pastry
Shortening, vegetable
Salt
Water, ice-cold
16 oz.
16 oz.
1 oz.
8 oz.
=
=
=
=
Dry mild solids
1 oz. =
4 c.
2 c.
8 t.
2 c.
c.
Use the recipe for basic pie dough. Convert the volume of the 1 c. ice-cold water to an equivalent weight measure using the
weight/volume information.
Basic Pie Dough
Weight/Volume Information
3 c.
1 c.
2 t.
1 c.
c.
Flour, pastry
Shortening, vegetable
Salt
Water, ice-cold
16 oz.
16 oz.
1 oz.
8 oz.
=
=
=
=
Dry mild solids
1 oz. =
4 c.
2 c.
8 t.
2 c.
c.
http://glencoe.mheducation.com/sites/0078690706/student_view0/math_quizzes2/math_quiz_3__pounds_and_ounces.html
12. Find the areas of the three triangles in the diagram below.
Density Calculations
UNITS OF DENSITY solids (g/cm3)
1. Find the unknown quantity:
a) d = 3 g/mL
V = 100 mL
M=?
𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
liquids (g/mL)
b) d = ?
V = 950 mL
M = 95 g
c) d = 0.5 g/cm3
V=?
M = 20 g
2. Find the unknown quantity (CONVERT FIRST to g or mL)
a) d = 24 g/mL
V = 1.2 L = _____ mL
M=?
b) d = ?
V = 100 mL
M = 1.5 kg = ______ g
c) d =
V = 0.52 L = ______ mL
M = 500 mg = ______ g
WORD PROBLEMS
1. A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?
2. Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder
weighs 306.0 g. From this information, calculate the density of mercury.
3. What is the weight of the ethanol that exactly fills a 200.0 mL container?
The density of ethanol is 0.789 g/mL.
4. A rectangular block of copper metal weighs 1896 g. The dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm. From
this data, what is the density of copper? (hint: find the volume of a block first)
5. What volume of silver metal will weigh exactly 2500.0 g. The density of silver is 10.5 g/cm3.
6. Find the mass of 250.0 mL of benzene. The density of benzene is 0.8765 g/mL.
7. A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weighs 1587 g. From this information,
calculate the density of lead.
8. 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10
mL mark, From this information, calculate the density of iron.
Name : ______________________________________________
Date: __________________________
Geometry A U8D4 Applications Using Conversions HOMEWORK
1. This is an extension of Problem 4 in the warm up. Using the diagram, draw grid lines to represent each
1
2
unit.
d.
How many squares do the new grid lines divide each unit square into?
e.
Use the squares described in part (a) to determine a lower estimate of area 𝑎 in the diagram. Find the area.
f.
Use the squares described in part (a) to determine an upper estimate of area 𝑎 in the diagram. Find the area.
g.
Calculate an average estimate of the area under the curve and above the 𝑥-axis based on your upper and lower estimates
in parts (b) and (c).
h.
Do you think your average estimate is more precise here than it was in the warm up? Explain.
2. Two right prisms have similar bases. The first prism has height 5 and volume 100. A side on the base of the first prism has
length 2, and the corresponding side on the base of the second prism has length 3. If the height of the second prism is 6, what is its
volume?
3. a. Calculate the area of the shaded figure below.
b. Explain how you determined the area of the figure.
4. In the following triangular pyramid, a plane passes through the pyramid so that it is parallel to the base and results in the crosssection △ 𝐴′𝐵′𝐶′. If the area of △ 𝐴𝐵𝐶 is 25 mm2 , what is the area of △ 𝐴′𝐵′𝐶′?
5) Change 48 oz. into pounds. 1 lb. 2 lbs. 3 lbs. 4 lbs.
6) Change 20 oz. into pounds and ounces. 2 lbs. 1 lb. 4 oz. 1 lb. 6 oz 1 lb. 8 oz
Convert 3 gal. to c. 24 c. 48 c. 60 c. 96 c
Convert 16 c. to gal.
Convert 2 c. to pt.
gal.
pt.
gal. 1 gal.
pt. 1 pt.
Convert 8 qts. to gal. 1 gal. 2 gal
gal.
pt.
gal. 3 gal.