1) A regular hexagon is inscribed inside a circle with a radius of 22 units. Find the area of the shaded region to the nearest hundredth (rounding final answer only).

2) The diagram below gives the dimensions of a swimming pool. If a cover is needed for the pool, approximately how much fabric will you need? Round your final answer to the nearest tenth.

3) Find the area of a cross-section 3 units from the center of a sphere with a radius of 5 units. Leave your answer in terms of pi.

4) In a solid cone, the base has a radius of 7 units and is sliced in half vertically from the top point. The area of the cross section created is 168 units2. Approximately what is the height of the cross section?

Name __________________________________ Date ______________________ Period _______

Chapter 12

Practice Problems

22 units • •

• •

•

• •

• 5 units

• 3 units

5) You are getting ready to eat a delicious sandwich you just made. The bread is rectangular with a length of 6 inches and a width of 8 inches. You stacked the sandwich so it is 2 inches tall. Before you eat it though, you like to cut your sandwich diagonally. Find the area of the cross-section formed.

6) The dimensions of Bria’s camping tent are shown below. a) How much fabric is needed to cover the entire tent (include the bottom of the tent).

b) The tent is not waterproof, so Bria wants to put a tarp over it in case it rains. The tarp will cover two of the tent’s rectangular faces. Which size tarp should she buy - the one that is 50 feet2, 100 feet2, or 150 feet2.

7) For Father’s Day, you decide to build your dad a bird house in the shape of a hexagonal pyramid. If you want each side of the base to have a length of 10 inches and a slant height of 15 inches, what is the total amount of materials you will need for the bird house?

8) The cylindrical glass is full of water and then poured into the rectangular pan. Will the water overflow when poured into the pan? Why or why not? Be sure to support your answer.

9) Cone Country Ice Cream Shoppe has mini cones with a diameter of 4 cm and a height of 4 cm. Cone country wanted to make a bigger cone that will hold 2.5 times more ice cream. The diameter will stay the same. Find the height of the large cone.

10) The top of a roof in the shape of a square pyramid has a side length of the base of 12 yards and is 1.6 times the height of another square pyramid with the same side length of the base. If the volume of the smaller roof is 240 yd3, what is the volume of the larger pyramid?

15 cm

15 cm

10 cm

8 cm

5 cm

11) A cylindrical glass soap dish is made by cutting a hemisphere out of a cylinder. How much glass is needed to create the dish? The measurements of the soap dish are on the diagram as below, listed in inches. Round your final answer to the nearest hundredth.

12) A baseball has a radius of approximately 1.5 centimeters while a basketball has a diameter of approximately 9 centimeters. How does the surface area of a basketball compare to the surface area of a baseball? Be very specific. It may be helpful to leave your answer in terms of pi.

13) You need to paint a child’s toy that is made up of a cylinder and hemisphere, as shown below. The radius of the cylinder is 14 cm and its altitude measures 30 cm. A small paint can covers 2000 cm2.

a) What is the surface area of the child’s toy? (Keep in terms of π.)

b) How many cans are needed to paint the surface if it requires two coats?

7

•

10

6

30 cm

14 cm

14) You have mastered solving a Rubik’s Cube. Now, you’re looking for a challenge and have discovered a spherical Rubik’s Cube. If the spherical Rubik’s Cube could fit inside the traditional Rubik’s Cube, and the traditional Rubik’s Cube has a volume of 185.193 cubic centimeters, what is the surface area of the spherical Rubik’s Cube?

15) Miss Day’s hall pass (wooden block) is in need of a new paint job. What should you use to determine how much paint is needed to cover the block? Specify if you should use surface area or volume and what type of shape you should use.

16) You need to fill the pool up with water. How would you determine how much water is needed to fill up the pool? Assume that the ends are semi-circles. Specify if you should use surface area or volume and what type of shape you should use.