3-D FiguresArea Surface Area
Volume
Circumference
Name: ______
Teacher: ______
Period: ______
Day 1 Classwork
Evaluating Formulas
Warm up:
Evaluate the following expressions:
1. 2x + 4 when x = 5 / 2. -2(x + 3) when x = 6 / 3. when x = 4Evaluate each formula below for the given values of the variables. Use the substitution property.
Plug it in – Plug it in!
1. Where d is the distance traveled by an object moving at speed r (rate) in time t. Find d, the distance, if r = 52m/sec and t = 8 sec. Formula: d = rt2. Where V is the volume of a rectangular solid with length l and width w and height h.
Find V if l = 12cm, w = 5cm, h = 3.5cm. Formula: V = lwh
3. Where P is the perimeter of a rectangle with length l and width w. Find P if l = 16km, w = 7.5km. Formula: P = 2l + 2w
4. Where S is the surface area of a cylinder with radius r and height h. Find S if r = 2ft and h = 3ft. Formula: SA =
5. Where d is the distance traveled by an object moving at speed r in time t. Find d if r = 40 and t = 8.
Formula: d = rt
Day 1 Homework
Evaluating Formulas
Evaluate the following formulas given the following information.
1. Where s is the distance in meters a free-falling object travels in t seconds. Find s if t = 4sec.Formula: s = 4.9t2
2. Where d is the distance traveled by an object moving at speed r in time t. Find d if r = 55 and t = 4. Formula: d = rt
3. Where P is the perimeter of a rectangle with length l and width w. Find P if l = 7 and w = 3.
Formula: P = 2l + 2w
4. Where S is the surface area of a cylinder with radius r and height h. Find S if r = 3ft and h = 4ft.
Round to the nearest tenth.
Formula: SA =
5. Where d is the number of diagonals of a polygon with n sides. Find d if n = 20.
Formula: d = n(n – 3)
6. Where I is the interest on an amount p, borrowed at an interest rate r for time t. Find I if p = 100, r = 0.06, and t = 1. Formula: I = prt
Day 2 Classwork
How do you find the radius and diameter of a circle when given the area?
Review: Find the area and circumference of the following circles.
1. Leave answer in terms of pi.r = ______d = ______
C = A =
5m
C = ______A = ______/ 2. Write answer to the nearest tenth.
r = ______d = ______
C = A =
12m
C = ______A = ______
3. Solve for r. (Round to the nearest tenth if necessary)
a) r2 = 64b) r2 = 100c) r2 = 26d) r2 = 46e) r2 = 76.4
4. Given the area, find the radius and diameter.
a) A = 49b) A = 81c) A = 16d) A = 25
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
e) A = 121f) A = 9g) A = 225h) A = 4
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
5. Given the area, find the radius and diameter.
a) A = 50.24sq. ftb) A = 452.4 sq. ftc) A = 12.42 sq. m
r = ______r = ______r = ______
d = ______d = ______d = ______
d) A = 314 sq. me) A = 706.9 sq. mf) A = 907.9 sq. m
r = ______r = ______r = ______
d = ______d = ______d = ______
Day 2 Homework
Find Radius and Diameter Given the Area
Read each of the following carefully. Underline the important information and show all work.
1. What is the diameter of a circle with an area equalShow all work.
to 113.04 sq. m? ______
What is the radius? ______
2. The area of a circle is 154 sq. m. What is the Show all work.
radius? ______
What is the diameter? ______
3. What is the area of a circle with a circumference of Show all work.
50cm? Leave your answer in terms of pi.
A) 2500B) 625C) 50 D) 25
4. What is the diameter of a circle with an area equal Show all work.
To 616sq. in?
A) 14inB) 28inC) 32inD) 48in
5. What is the circumference of a circle with an areaShow all work.
of 81 sq m? Leave answer in terms of .
A) 40.5mB) 26mC) 9mD) 3m
6. What is the circumference of a circle with an area of 169sq cm? Leave your answer in terms of .
7. Chef Pierre uses vegetables grown in his new circular garden. He knows that the area of his garden is 15 square meters. He wants to build a path through the middle of the circular garden. What will be the approximate length of the new path?
New path design
A) 1.2mB) 2.2mC) 4.4mD) 7.2m
Day 3 Classwork
Find Radius or Diameter Given the Circumference
Warm up:
1. Find the Circumference if the diameter is 20in. Leave answer in terms of pi. / 2. Find the Circumference if the radius is 3m. Write answer to the nearest tenth.Remember the Formula:
3. Given the circumference, find the radius and diameter:
a) C = 4b) C = 20c) C = 50d) C = 100
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
e) C = 80f) C = 25g) C = 36h) C = 62
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
4. Given the circumference, find the radius and diameter:
a) C = 81.7mb) C = 94.2mc) C = 18.8 ftd) C = 188.5 ft
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
e) C = 50.3mf) C = 150.8 ftg) C = 12.6mh) C = 100.5 ft
r = ______r = ______r = ______r = ______
d = ______d = ______d = ______d = ______
Day 3 Homework
Find the Radius and Diameter Given Circumference or Area
andRemember the formulas:
1. If the Circumference of a circle is 20, find r = ______
d = ______
Area = ______
(to the nearest tenths)
2. If the Circumference of a circle is 31.4, find r = ______
d = ______
Area = ______
(in terms of)
3. If the Area of a circle is 36, find r = ______
d = ______
Circumference = ______
(to the nearest tenths)
4. If the Area of a circle is 153.9, find r = ______
d = ______
Circumference = ______
(in terms of )
5. If the Circumference of a circle is 157.1, find r = ______
d = ______
Area = ______
(to the nearest tenths)
Extended Response:
6. Joe ordered a pizza with an area of 63.585 sq. in. Karen ordered a pizza with a circumference of 28.26in. Whose pizza has the greater distance? Show all your work!
Explain how you found which pizza has the greater distance:
______
Day 4 Classwork
3-D Figures
______are the flat sides of a three-dimensional figure
A ______has two parallel bases that are congruent polygons.
Fill out the following chart:
Picture / Name of 3D Figure / Name of Base Shape / Number of Bases / Number of FacesA ______is a flattened object with surface areas that can be folded into a three dimensional figure.
Look at the net and name the 3-D figure.
1.2.3. 4.
______
A polyhedron is a solid with only flat surfaces. List some polyhedrons.
a) ______b) ______c)______d) ______
Is a cylinder a polyhedron? ______
Day 4 Homework
3-D Figures
1. How many faces and bases does a rectangular prism have?
Faces: ______Bases: ______
2. What is the base shape of a cylinder?
______
3. Which of the following describes the distance around a circle?
A) VolumeB) CircumferenceC) Surface AreaD) Radius
4. What is the circumference of the circle?
5in
A) 15.7inB) 314inC) 31.4inD) 78.5in
5) The circumference of a circle is 30. What is the radius of the circle?
A) 30B) 60C) 15D) 900
Determine if the following is rational or irrational:
6) 7) 48.5962…8) 9) 010) 2
______
11) Between which two consecutive integers is ?
A) 7 and 8B) 8 and 9C) 9 and 10D) 10 and 11
12) The sum of -30 and what number is 24.
A) -6B) -54C) 16D) 54
13) Convert 45 degrees of a circle to a percent.
A) 45%B) 12.5%C) 160.2%D) 50%
14) The area of a circle is 144. What is the diameter of the circle?
A) 144B) 12C) 6D) 24
15) If the sum of three angles of a quadrilateral is 2730, what is the measure of the fourth angle?
A) 870B) 900C) 70D) 270
Day 5 Classwork
Volume of 3-D Figures
Rectangular Prism:
Formula:
l = length
Heightw = width
Widthh = height
Length
Find the volume for each of the rectangular prisms:
1.6.5cm5cm
9cm
/ 2.
5in
2in
8in
3.
3m
3m
11m
/ 4.
15ft
4ft
7ft
Day 5 Classwork
Volume of 3-D Figures
Cylinder: Radius (r) Formula:
Height (h)
Find the volume for each of the cylinders:
1.4m
12m
/ 2. 2.5ft
9ft
3. 4in
7in / 4.
20mm
8mm
Day 5 Homework
Volume of 3-D Figures
Find the volume of the following 3-D Figures:
1.4m
2m
15m
/ 2.
3in
10in
3.
8mm
20mm
/ 4.
10ft
2ft
4.5ft
Day 6 Classwork
Surface Area Discovery
Measure each edge of the net with the ruler. Using these measurements, find the area of each separate rectangle.
1.
A = ______
2.3. 4.
A = ______A = ______A = ______
5.
A = ______
6.
A = ______
Day 6 Classwork
Surface Area Discovery
Using the net figure, add up each rectangle’s area:
1) ______+ 2) ______+ 3) ______+ 4) ______+ 5) ______+ 6) ______
Total Area of net = ______
The sum of the areas of the faces in a rectangular prism represents the Surface Area!
Let’s try using the Surface Area formula for a Rectangular Prism:
SA = ______.
Try this:
Length = 6in Width = 3inHeight = 4in.
Find the Surface area using the dimensions above.
Day 6 Homework
Surface Area Discovery
3in
1.
3in
3inArea ______
2.
3inArea ______3in
3in3in
3.4.5.
3in3in
Area ______Area ______Area ______
6.
3in
Area ______3in
1. Find the Area for each square in the figure:
1. ______2. ______3. ______4. ______5. ______6. ______
2. Add up the area of each square to find the total surface area:
______+ ______+ ______+ ______+ ______+ ______= ______
3. What type of 3-D Figure is the above net?
______
4. Using the following Surface Area formula, find the total Surface Area for the above figure
Formula: where s = side of square.
Surface Area = ______
Day 7 Classwork
Surface Area of Rectangular Prisms and Cubes
To find the Surface Area of a Rectangular Prism follow this formula:
Remember: “l” is length, “w” is width, and “h” is height.
1. l = _____w =_____
h = _____
10mm
3mm
5mm / 2.
9in
6in
12in
l = _____
w = _____
h = _____
3.
20cm
16cm
30cm
/ 4.
14in
7in
12in
Day 7 Classwork
Surface Area of Rectangular Prisms and Cubes
To find the Surface Area of a Cube follow this formula:
Remember: “s” is sides
1.5in
/ 2.
12m
3.
2mm
/ 4.
20cm
Day 7 Homework
Surface Area of Rectangular Prisms and Cubes
Remember the formulas:
Right Rectangular Prism:
Cube:
1.5in
3in
10in
Find the Surface Area:
Find the Volume: / 2.
15cm
Find the Surface Area:
Find the Volume:
3. Describe the difference between surface area and volume:
______
4. List two real – life examples of surface area.5. List two real – life examples of volume.
a. ______a. ______
b. ______b. ______
Day 8 Classwork
Surface Area of a Cylinder
To find the Surface Area of a Cylinder use this formula:
Remember: “r” is radius and “h” is height.
1.5in
8in
/ 2.
20mm
25mm
3. A can has a diameter of 8 inches and is 10 inches tall. What is the surface area?
4. A cylinder has a radius of 13cm and a height of 22cm. Find its surface area.
*5. When finding the surface area of opened can (cylinder), would your formula change? Why?
______
Day 8 Homework
Surface Area of a Cylinder
Use the Reference Sheet for Formulas!!!
Find the Surface Area and Volume for each:
1.3cm
8cm
Find the Surface Area:
Find the Volume: / 2.
30m
10m
Find the Surface Area:
Find the Volume:
3. A quarter is really a very short cylinder. Its height is about 1mm and its diameter is about 24mm. Find the surface area of a quarter.
4. Mary is wrapping a can of paint as a gag gift for a friend. If the can is 11 inches high and has a diameter of 7 inches, how many square inches of wrapping paper will she use in completely covering the can?
Day 9 Classwork
Estimating Surface Area
Warm – up
Determine if the given example is surface area of volume.
1. Wrapping a present______
2. Filling a jar with candy______
3. Painting a model home______
4. Filling a cylinder pot with soil ______
Estimation: Round BEFORE you solve!!! (Think Estimation – Easy)
Estimate the following to the nearest whole number:
1) 42.3 ______2) 12.7 ______3) 3.1415926535… ______4) 9.1 ______
5) 6.5 ______6) 2.1 ______7) ______8) 19.9 ______
Remember: Estimate ALL numbers including!!
Estimate Surface Area / Estimate Volume1.
3.1m
5.6m
2.2m / l = ___ w = ____ h = ____ / l = ___ w = ____ h = ____
2. 5.1cm
11.8cm / r = ___ h = ____ = ____ / r = ___ h = ____ = ____
3.
6.3cm
5.8cm
9.4cm / l = ___ w = ____ h = ____ / l = ___ w = ____ h = ____
4. What is an estimate for the surface area of a rectangular prism with a length of 2.5 in, a width of 6.7in, and a height of 3.6in?
Day 9 Homework
Estimating Surface Area
Estimate the surface area for each of the following:
Estimate Surface Area / Estimate Volume1. 3.9m
2.1m / r = ___ h = ____ = ____ / r = ___ h = ____ = ____
2.
2.7cm
1.8cm
1.8cm / l = ___ w = ____ h = ____ / l = ___ w = ____ h = ____
3. 1.9cm
10.4cm / r = ___ h = ____ = ____ / r = ___ h = ____ = ____
4.
3.5in
2.6in
8.3in / l = ___ w = ____ h = ____ / l = ___ w = ____ h = ____
5. What is an estimate for the surface area of a cylinder with a height of 4 ft and a radius of 2 ft?
Name______
1.Find the surface area for the following solid.
Write the formula, the givens, and show all work.
Remember to use this formula: SA = wh + lw + lh + ls
1.
2.
3. Estimate the surface area.
Volume and Surface Area Review
*Remember to use the Reference Sheet for Formulas!!
Surface Area / Volume1.
6in
5in
10in / SA = / V =
2.
6in
15in / SA = / V =
3.
16m
5m
7m / SA = / V =
4. 16cm
12cm / SA = / V =
Name______Period______
For each figure below: a) Name the figure.b) Name the shape of the base.
7) Estimate the surface area of the
rectangular prism.
9) The volume of a cube is 27cm.
What is the length of each side?
11) Use the figure below to answer
the following questions:
16) If a circle has an area of 144π, what is the diameter?
17) If a circle has a circumference of 10π, what is the diameter?
#18 – 19 Find the surface area and volume for the following figures:
Surface Area / Picture / Area20) a) If the volume of a cylinder is 350 in and it costs $0.25 per cubic inch to fill it
with soda, what is the cost of filling the cylinder?
b) If the volume of a cylinder is 1000 in and it costs $0.50 per cubic inch to fill
it with candy. What is the total cost of filling the cylinder?
Review
Evaluate.
21) 5 – 2022) 6 – 2423) 24)
25) 6 – (-10)26) -8 - 27) =_____28)
29) Between which two consecutive numbers does lie? _____ and _____
1