Unit 9 HW Packet

HW 9-1

1. Which of the following ratios describes pi?

a)

b)

c)

d)

2. Find the area of the rhombus in the diagram if the measurements are given in inches.

For problems 3 - 7 find the measurements.

3. 4.

5. 6. the diameter of circle G in which C = 10 ft.

7.

21

29

8. Skeeter, the wonder dog, jumps through circular rings as part of his dog show exhibition. Skeeter

requires a width of 18 inches for his costume to clear the ring. Will a ring with an inner circumference

of 39.8 inches be large enough for Skeeter's act?

9. A large pizza has a circumference of 72.5 inches. What is the area of the smallest possible box that

would be able to hold the pizza? (NOTE: each side has lengths that are whole numbers).

10.

11. Find the circumference of each circle. Round your answers to the nearest thousandth, if necessary.

HW 9-2

1. Find the area in terms of π.

2. Find the circumference of circle P in

which A = 36π in2.

3. Find the area. Round your answer to the nearest tenth.

4. Find the missing measurement for each circle. Give your answers in terms of π.

5. Explain, informally, how to derive the formula for the area of a circle. Use a diagram to help in

your explanation.

6. What is the circumference of a circle whose area is 64π in2?

7. Find the area of the parallelogram below.

8. Find the area of an equilateral triangle with a side length of 3 in.

9. Find the composite area of each of the following figures. Leave your answers in terms of pi, if

necessary.

a) b)

8. Find the shaded area of the each of the following figures. Leave your answers in terms of pi, if

necessary.

a) b)

c) d) This figure is a square with four quarter-

circles

HW 9-3

1. All sides of the triangle are multiplied by 3. What happens to the area of the triangle?

2. What happens to the area of the triangle if the height is doubled?

3. What happens to the area of a trapezoid with base lengths 12cm and 18 cm and height 5 if

the height is multiplied by 1/3?

4. A square has an area of 36 m2. If the area is doubled, what happens to the side length?

5. A circle has a diameter of 14 ft. If the area is tripled, what happens to the circumference?

6. What happens to the circumference of a circle with center (0,0) that passes through (5,0) if

the radius is multiplied by 3/5?

7. A circle has a circumference of 16 mm. If you multiply the area by 1/3, what happens to

the radius?

HW 9-4

1. Fill in the blank: A ____________ has two circular bases. (prism, cylinder or cone) Classify each figure. Name the vertices, edges and bases.

____________________ ____________________ ____________________

____________________ ____________________ ____________________

____________________ ____________________ ____________________

____________________ ____________________ ____________________

5. Describe the faces of a cube: __________

6. Describe the faces of a rectangular pyramid: __________

7. Explain why a cylinder is not a polyhedron: __________________________________

____________________________________________________________________

8. Name the number of vertices, edges and faces for each polyhedron.

Vertices: Vertices: Vertices: Edges: Edges: Edges: Faces: Faces: Faces:

Vertices: Vertices: Edges: Edges: Faces: Faces:

HW 9-5

1. For each shape, describe (in a picture or in words) a cross section taken a) parallel to the base b) perpendicular to the base

2. Describe each cross-section.

__________ __________ __________ __________

3. Which shape best represents a hexagonal prism when viewed from the top?

4. Describe the cross section obtained by cutting a plane through the diameter of the base and perpendicular to the base of a right cylinder. __________

5. A 2 x 10 rectangle is revolved around the side of length 2. Draw the resulting solid.

6. A right triangle with leg lengths 3 and 11 is revolved around the side of length 11. Draw the resulting solid.

7. A piece of cheese is a prism with equilateral triangular bases. How can you slice the cheese to make each shape? a) an equilateral triangle? b) a rectangle?

8. A loaf of bread is in the shape of a cylinder. If you cut the bread into slices, what are the possible shapes of those slices? Draw a picture to support your answer.

9. Find the area of the composite figure to the nearest square centimeter.

10. A factory is building a box for a new product. The box is a cube, as seen in the diagram. Once the box is made, the manufacturers decided to triple the length of each side. What does this do to volume of the box?

HW 9-6 1. Given an informal explanation for the formula for the volume of a cylinder, based on the formula for the volume of a prism. Find the volume of each prism.

1. A cube with edge 2. length 8 ft.

3. Find the volume of a cylinder with base 4. Find the volume of the cylinder. area 25 cm2 and height 3cm more than the radius. 5. Find the total volume 6. (round to the nearest tenth).

HW 9-7

1. Find the volume of the pyramid.

2. Find the volume of the figures below. Give your answer in terms of and rounded to the nearest

tenth.

a) b) c)

3. Find the volume of the composite figure to the right. Round to

the nearest tenth if necessary.

4. Use the diagram below to explain the formula for the volume of a pyramid.

HW 9-8

1. Find the volume of each of the following figures. Round your answers to the nearest tenth.

a) b) c)

2. Find the diameter of the sphere with volume 7776 in3.

3. Find the volume of the composite figures below. Round your answers to the nearest tenth.

HW 9-9

1. Happy" brand peanut butter is sold in differing size cylindrically shaped jars. While buying a

larger quantity of an item usually means a reduced unit price, purchasing larger jars of peanut butter does not always mean a savings. Let's test Happy peanut butter to see which jar is the better buy. Justify your answer.

2. A cylindrical container that is 10 inches in diameter is required to hold 10 gallons of water.

Find the height of the container to the nearest tenth of an inch, if one gallon of water occupies

231 cubic inches of space.

3.

The large jar is 7

inches tall,

has a diameter

of 5 inches,

and costs $7.50

The smaller jar

is 4.5 inches

tall, has a

diameter of 3

inches, and

costs $1.99.

4. Students in one mathematics class noticed that a local movie theater sold popcorn in different

shapes of containers, for different prices. They wondered which of the choices was the best

buy. Analyze the three popcorn containers below. Which is the best buy? Show work and

Explain your answer.

5. A rectangular piece of wood measures 3.0 cm by 6.0 cm by 4.0 cm and has a mass of 80.0

grams. What is the density of the wood? If the density of water is 1.00 g/cm3, will the piece

of wood float in water? (Hint: Items float if they are less dense)

6. I threw a plastic spherical ball in the pool for my dog to fetch. The mass of the ball was 125

grams.

a. What must the volume have been in order for the density of the ball to be 0.5 g/mL?

b. Given your answer to part a, find the radius of the ball, to the nearest tenth.

HW 9-10

1. Name a figure that has 1 circular base. ___________________

2. Name a figure that has 2 circular bases. _________________________. 3. How many faces does a hexagonal prism have? ___________

4. What happens to the area of a trapezoid with bases 5 and 6 and height 4 if the height is multiplied by 4?____________________

5. What happens to the area of a triangle if the base and height are multiplied by 5? ______________ 6. What shape is the cross section of a cone taken parallel to the base? _________________

7. What shape is the cross section of a cone taken perpendicular to the base? _______________

8. A right triangle with leg lengths 3 and 4 is revolved around the side of length 4. Draw the result.

9. What is the volume of the cone in terms of .

10. What is the volume of the cylinder in terms of ?

10 in.

13 m