Assignment 6.1: Pythagorean Theorem **Round all answers to two decimal places**

1. Solve for the missing side in the following triangle:

2. A wall is supported by a brace 10 feet long, as shown in the diagram below. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?

3. When Arnold swims laps in his rectangular swimming pool, he swims along the diagonal so he doesn’t have to turn around so often. Find the distance Arnold travels by swimming once along the diagonal.

4. The three sides of a triangle are 18 cm, 24 cm and 30 cm. Determine whether the triangle is a right triangle. Justify your answers using calculations.

5. Determine the value of x and y.

6. Towns A, B, C, and d are situated as shown on the diagram. a. How far is it from town B to town D? b. How far is it from town B to town C?

3.2m

9.8m

40

cm

30

cm

7Km

6Km

10Km

B

A C

D

Assignment 6.2: Composite Shapes **Round all answers to the nearest hundredth**

1. Use the figure on the right to answer the questions.

a) What is the area of the square?

b) What is the area of the triangle on the left?

c) What is the area of the composite figure?

2. Find the area of the following shaded regions.

a)

b)

3. Determine a simplified expression for the perimeter and area of the figure to the right.

4. A figure is a triangle composed of and a square, as shown below. The area of the square is 144 m2. What is the height of the triangle? Show your work.

5. The figure below is made two semicircles. What is the area of the shaded region? Show your work.

6. A circle and a triangle of an equal area. If the circle has a radius of 4cm and the triangle has a height

of 15cm, determine the base of the triangle. 7. The area of a triangle is 32 cm2. If the height of the triangle is 7 inches, then what is the base of the

triangle?

8. The base of a parallelogram is 17mm. If the area of the parallelogram is 82mm2, what is the height of

the parallelogram?

9. The area of a rectangle is 42cm2. If the length of the rectangle is 5cm, what is the perimeter of the

rectangle?

10. A right-angle triangle has a height of 6 inches and hypotenuse of 9 inches. What is the area of the

triangle?

Assignment 6.3: Volume of Prisms & Cylinders **Round all answers to the nearest hundredth**

For questions 1-4, find the volume and surface area of the shape drawn.

1.

2.

3.

4.

5. Dairy Fresh packages two cartons of milk. The large carton is 8cm by 8cm by 18cm. The small

carton is 6cm by 6cm by 8cm. How many small cartons of milk would fill one large one?

6. A gold bar is 15 cm by 8cm by 3cm and is worth $350 000. What is the volume of the bar in cubic centimetres? How much is one cubic centimetre work?

7. A cylinder just fits inside a 10cm by 10cm by 10cm box. a) Determine the volume of the box. b) Determine the volume of the cylinder. c) Determine the volume of the empty space in the box when the cylinder is placed inside.

8. Tracy plans to create an ice sculpture for a table centrepiece at her friend’s housewarming. The ice she will start with is shown. Calculate the volume of ice Tracy will need to make the sculpture.

9m

9m

10m30ft

6 ft5 mm

12mm 12in5 in

10in

5 cm

3 cm

4cm

2cm

5 cm

Assignment 6.4: Surface Area of Prisms & Cylinders **Round all answers to the nearest hundredth**

1. Calculate the surface area of the following shapes.

a) b)

2. A can of soup is 10.3cm high and its diameter is 6.7cm. How much paper is needed to make the label?

3. A wedge of cheese is in the shape of a triangular prism. It is 6cm high and each triangular face has

a side length of 10cm and a base of 2.9cm. (a) How much plastic wrap is needed to cover the cheese? (b) The plastic wrap costs $0.01/cm2. What is the cost to package the cheese?

4. Find the surface area of the following composite shape.

5. A box with a square base must have a volume of 200cm3. Find the dimensions of the box that minimizes the amount of material used.

12.5 m

23 m

25 m

24 m

13 m

24 m

15 in.

18 in.

Assignment 6.5: Volume of Cones, Spheres, and Pyramids **Round all answers to the nearest hundredth**

1. Calculate the volume of each solid. a) b)

c) d)

2. Calculate the volume of a sphere with a diameter of 78 cm.

3. Calculate the volume of the figure shown in the diagram to the right

4. A sphere with a radius of 46 cm is centered inside a sphere with a radius of 76 cm. What is the volume of the space between the two spheres?

5. A sculptor wants to remove stone from a cylindrical block 3 feet high and turn it into a cone. The diameter of the base of the cone and cylinder is 2 feet. What is the volume of the stone that the sculptor must remove?

Assignment 6.6: Surface Area of Cones, Spheres, and Pyramids **Round all answers to the nearest hundredth**

(HINT: drawing the shape first will help you visualize the object)

1. A tennis ball has a diameter of 6.7 cm. What is its surface area?

2. Find the surface area of a cone with a diameter of 13.6 cm and a slant height of 9.8 cm.

3. Find the surface area of an open pipe that has a diameter of 4.5 cm and is 18.8 cm long.

4. Find the surface area of a hemisphere with a radius of 18.5 cm.

5. Find the total surface area of a cone with a radius of 16 inches and a height of 20 inches.

6. Find the surface area of the shape shown in the following diagrams.

a)

b)

Assignment 6.7: Surface Area and Volume with Algebra **Round all answers to the nearest hundredth**

1. A cylindrical juice container has a diameter of 8cm. If the surface area of the juice container is 754cm2, what is the height of the container?

2. Determine the height of a cone if the volume of the cone is 56cm3 and the diameter is 5cm. 3. If a can of soup can hold 64cm3 of soup, and the height of the container is 6cm, what is the radius of

the filled can of soup? 4. A circle and a triangle of an equal area. If the circle has a radius of 4cm and the triangle has a height

of 15cm, determine the base of the triangle. 5. Find the height of a can with a surface area of 326.73 cm2, if the radius is 4cm.

6. If the volume of a square-based pyramid is 680 cm3 and the side lengths of the square are 16 cm, what is the height of the pyramid?

7. A gift is put into a rectangular box measuring 6 x 6 x 15 inches. If each wrapping paper sheet covers

60 in2, how many sheets must be purchased to completely wrap the gift?