190 CHAPTER 4 Geometry

Transcription

1 90 CHAPTER 4 Geometry. Convert 75.4 mm to cm.

2 SECTION 4.0 CLAST-Like Questions mm to cm. a) cm b) 7.54 cm c) 75.4 cm d) 754 cm. Round measurement A to the nearest ½ inch. a) inches b) inches A c) inches 4 d) 3 inches 3. Find the distance around a circular table of radius.3 m. a).6 π m b).69 π m c).96 π m d).3 π m 4. Find the distance around the figure. 8 cm 5 cm " " a) 38 + π m b) π m c) π m d) π m 5. The length of a recta ngle is 5 feet more than twice the width. If th e perimeter is feet. Find the length of the rectangle. a) ft b) 9 ft c) 4 ft d) 8 ft 6. Find th e area of the figure below. 4 in a) π sq in b) π in c) π in d) π sq in

3 9 CHAPTER 4 Geometry 7. Find the shaded area. 5 m 0 m a) 50 m b) 5 m c) 75 m d) 50 m 8. How many square yards of carpet are needed to cover a room that is feet long by 5 feet wide? a) 60 sq ft b) 0 sq yds c) 60 sq yds d) 80 sq ft 9. A ball has a radius of 5 inches, how much air in cubic inches can it hold? a) 5π inches b) 66 3 π inches c) 66 3 π cub. inches d) 5 π cub. inches 0. Find the volume of the cone. cm 9 cm a) π cm 3 b) 36 π cm 3 c) 6 π cm 3 d) 8 π cm 3. Jan is covering a gift box that is in the shape of a cube of side 0 cm. How much paper, in cm, does Jan need? a) 0 cm b) 60 cm c) 00 cm d) 600 cm. What is the appropriate measure for the paper covering a 6-ounce soda bottle? a) liters b) miles c) square inches d) cubic meters 3. What is the appropriate measure for the amount of water in a pool? a) liters b) square inches c) miles d) meters

4 SECTION 4.0 CLAST-Like Questions What is the appropriate measure for the distance walked to school? a) liters b) square inches c) miles d) cubic meters 5. Find the angle measurements if lines L and L are parallel. L L 5x - 0 3x a) 5 º b) 5 º, 75 º c) 75 º, 05 º d) 05 º 6. Find the angle measure of x. x y z 0 º a) 40 º b) 70 º c) 0 º d) 40 º 7. Find the measure of one angle of a regular hexagon. a) 60 º b) 0 º c) 80 º d) 70 º 8. Find the angle measure of x. 0 º x a) 70 º b) 90 c) 0 º d) 80 º 9. Are the triangles similar? 95 º 35 º 50 º 95 º a) yes b) no

5 94 CHAPTER 4 Geometry 0. Find the height of a flagpole that casts a shadow of 5 feet while a person who is 6 feet tall casts a shado w of 3 feet. a) feet b) 4 ft c) 8 ft d) 0 ft. Find the missing leg of the triangle. 3 cm 5 cm a) 8 cm b) cm c) 44 cm d) 94 cm. A boat leaves a dock and sails 4 miles west and 0 miles north. How far is the boat from the dock? a) 34 miles b) 68 miles c) 6 miles d) 67 miles 3. How high up a wall does a 50-foot ladder reach if the foot of the ladder is 30 feet from th e wall? a) 30 feet b) 40 feet c) 600 feet d) 3400 feet 4. What quadrilateral has all sides equal, but no right angles? a) square b) rectangle c) rhombus d) trapezoid 5. Find the value of x. 3x + 0 x a) 34 b) 68 c) d) 80

6 SECTION 4.0 CLAST-Like Questions 95 Answers to CLAST-LIKE QUESTIONS 4.0 Explanations. c 6. d. d 6. a. b. b 7. b. c 7. b. c 3. a 8. b 3. a 8. a 3. b 4. b 9. c 4. c 9. a 4. c 5. b 0. a 5. c 0. d 5. a. Recall the metric sy stem: km hm dam m dm cm mm cm is one place to the left of mm. Therefore, move the decimal point one place to the left, giving us 75.4 cm. The unit specified is ½ inch. A is between and ½ inches. A is nearer to ½ inches. 3. Circumference (C) of a circle: C = π r = π (.3 m) =. 6π cm 4. The figure has 3 sides that are line segments and one part that is half of a circle. Recall that perimeter is the distance around a figure. See below. P = 5 cm + 8 cm + 5 cm + ½ circumference of circle = 5 cm + 8 cm + 5 cm + ½ ( π)(8 cm) = 38 cm + 4π cm = π cm 5. Let x represent the width. Then the length is x + 5. Perimeter (P) of a rectangle: P = L + W and we know that P =. P = (x + 5) + x = 4x +0 + x = 6x = 6x = 6x = x The length is () + 5 = = 9 feet 6. The figure consists of a square and four half circles (or two full circles). To find the area (A), recall the area of a square and the area of a circle. The length of one side is 4 in, and the radius of each circle is in. A = s + π r + π r A = (4 in) + π ( in) + π ( in) = 6 in + 4π in + 4π in = 6 in + 8π in = 6 + 8π sq in

7 96 CHAPTER 4 Geometry 7. Area (A) of shaded region = Area of rectangle Area of triangle A = LW ½ ( b )( h ) A = 0 ( 5 ) ½ ( 0 ) ( 5 ) = 50 5 = 5 m 8. Change feet to yards. feet = 3 = 4 yards and 5 feet = 5 3 = 5 yards. Now find the area (A) of the floor. A = LW A = (4 yards) (5 yards) = 0 sq yds 9. Cubic inches imply volume. We need to find the volume ( V ) of air that the ball holds. 0. Volume (V) of a cone = π r h 3 4 V = π r V = π (5 in) 3 4 = π (5 in 3 ) = π in 3 = 3 66 π cub.in 3 V = π 3 ( cm) (9 cm) = V = π cm 3 π 3 (4 cm ) (9 cm) = π 3 (36 cm 3 ). cm implies area. We need to find the surface area ( S ) of the box. Note that the box is shaped like a cube. S = 6 (side) S = 6 (0 cm) = 6 (00 cm ) = 600 cm. Area is the measurement, and area is measured in square units. The only square unit measure given is square inches. 3. The amount of water is a liquid measure. The for liquid measure is liters. only measure given which is appropriate 4. Distance is a linear measure. Miles is the appropriate measure.

8 SECTION 4.0 CLAST-Like Questions The acute angle and the obtuse angle are supplementary. 3x + 5x 0 = 80 8x 0 = 80 8x = x = 00 x = 5 The acute angle measures 3( 5 ) = 75 º. The obtuse angle measures 5( 5 ) 0 = 5 0 = 05 º. 6. x and 0 º are supplementary. 0 º + x = 80 º x = 80 º 0 º = 70 º The triangle is an isosceles triangle. Therefore, the angle measurement of y and z are equal. The sum of the angles in a triangle is 80 º. x + y + z = 80 º x + 70 º + 70 = 80 º x + 40 º = 80 º x = 80 º 40 º = 40 º 7. A hexagon has six sides. First find the sum of angles. 80(6 ) = 80(4) = 70 º. The sum of angle s of a hexag on is 70 º. To find the value of just one angle, divide the sum by º 6 = 0 º. 8. The sum of angles in any quadrilateral is 360 º. 90 º + 90 º + 0 º + x = 360 º 90 º + x = 360 º x = 360 º 90 º = 70 º 9. In similar triangles, corresponding angles are equal. In the small triangle, let the missing angle be x. 50 º + 95 º + x = 80 º 45 º + x = 80 º x = 80 º 45 º = 35 º The angles are 50 º, 95 º, and 35 º. In the big triangle, let the missing angle be y. 95 º + 35 º + y = 80 º 30 º + y = 80 º y = 80 º 30 º = 50 º The an gles are 95 º, 35 º, and 50 º. Note that for both triangles, corresponding angles are equal. Therefore, the triangles are similar.

9 98 CHAPTER 4 Geometry 0. Flagpole (x) person (6 ft) 5 ft 3 ft shadow shadow The triangles are similar. Therefore, the sides are proportional. Use the ratio the proportion. x 5 = 6 3 3x = 30 x = 0 ft big small to set up. The triangle is a right triangle. To find the length of the missing leg, a, use the Pythagorean Theorem. a + b = c a + 5 = 3 a + 5 = 69 a = 69 5 a = 44 a = 44 a = cm. BOAT 0 miles c 4 miles DOCK We have a right triangle and can use the Pythagorean Theorem. a + b = c = c = c 676 = c 676 = c 6 miles = c

10 P + P + P = P = SECTION 4.0 CLAST-Like Questions Wall 50 ft This is a right triangle. Use the Pythagorean Theorem. Ladder a P 30 P 50 P a P 900 = 500 a P = 600 = feet a = 40 feet a 4. A quadrilateral with all sides equal is either a square or a rhombus. But, a square has right angles. Rhombus is the correct answer. 5. The consecutive angles are supplementary. x + 3x + 0 = 80 5x + 0 = 80 5x = x = 70 x = 34