Name Free Response Review 1. A rescue team 1000 ft. away from the base of a vertical cliff measures the angle of elevation to the top of the cliff to be 70. A climber is stranded on a ledge. The angle of elevation from the rescue team to the ledge is 55. How far is the stranded climber from the top of the cliff? (Hint: Find y and w using trig ratios. Then subtract w from y to find x). Round to the nearest foot. 2. A person in an apartment building sights the top and bottom of an office building 500 ft. away. The angle of elevation for the top of the office building is 23 and the angle of depression for the base of the building is 50. How tall is the office building? Round to the nearest foot. y x w 1000 500 3. A ladder on a fire truck has its base 8 ft. above the ground. The maximum length of the ladder is 100 ft. If the ladder s greatest angle of elevation possible is 70, what is the highest above the ground that it can reach? Round to the nearest foot. 100 8
4.Find the SURFACE AREA and VOLUME of each pyramid below. a. b. 8 m 10 in 4 m c. 9 5a. An aquarium shaped like a rectangular prism has length 30 ft., and width of 10 ft., and a height of 20 ft. If you fill the aquarium 75% full with water, how many cubic feet of water will the tank contain? 24 b. When you submerge a rock in the aquarium, the water level rises 1 4 ft. Find the volume of the rock. c. How many rocks of the same size can you place in the aquarium before the water overflows and spills out? d. How many aquarium tanks with length 5 ft., width 2 ft., and height 4 ft. can you fill using the same amount of water (in cubic feet) as the tank in part (a)?
6a. A painter to wants to paint the house with the dimensions labeled below. How much paint will he need to cover everything except the shingled roof? 12 m 9 m 9 m 14 m b. If a gallon of paint covers 150 square meters, how many gallons of paint will he need to buy? c. If it costs $28 a gallon, how much is it going to cost (remember you cannot buy just part of a gallon of paint)? 7. You and your friends are off to the beach and wish to build a sand castle. You bring two pails with you. The first is circular and has a base with a circumference of 4 inches, is ches tall, and has an opening on top that is twice the diameter of the base. The second pale has a square base with side lengths of 3 inches, a height of 14 inches, and an opening at the top that is twice the side length of the base. a. Label the diagrams that represent each pail. b. How much sand will fit in each pail? c. Which pail will require fewer scoops of sand to build sand castles? How much faster is this pail at scooping sand?
8. Shayna designed her perfect wedding cake. She wants to have 3 layers with smooth white frosting on the cake. The first layer will have a 24-inch diameter, the second layer will have an 18-inch diameter, and the top layer will have a 10-inch diameter. Each layer will be 6 inches tall. How many square inches of frosting will show on the cake? 9. Find the surface area and volume of each composite solid. a. b. 6 in 5 in 13 in 6 in 8 in 5 in
Answers 1. 1319 ft 2. 808 ft 3. 102 ft 4a. SA = 384 in 2, V = 384 in 3 4b. SA = 96 24 3 m 3, V = 16 39 m 3 4c. SA = 1296 units 2, V = 1728 units 3 5a. 4500 ft 3 b. 75 ft 3 c. 20 rocks d. 112 tanks 6a. 522 m 2 b. 4 gallons c. $112 7b. Pail 1: 112 352 in 3, Pail 2: 294 in 3 c. 1 st pail; 58 in 3 faster 8. 456 1432.6 in 2 9a. SA = 210 in 2, V = 400 in 3 b. SA = 288 in 2, V = 336 in 3