Perimeter, Area, Surface Area, & Volume

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1 Additional Options: Hide Multiple Choice Answers (Written Response) Open in Microsoft Word (add page breaks and/or edit questions) Generation Date: 11/25/2009 Generated By: Margaret Buell Copyright 2009 Study Island - All rights reserved. 1. Perimeter, Area, Surface Area, & Volume If R = 3 inches and H = 8 inches, what is the surface area of the cylinder? A in. B in. C in. D in. 2. If R = 3 inches and H = 8 inches, what is the volume of the cylinder? 1 of 11 11/25/09 2:59 PM

2 A in B in C in D in 3. Estimate the perimeter of the figure above. A. 26 cm B. 16 cm C. 10 cm D. 24 cm 4. In the figure above, the radius of circle C is 2 cm. What is the approximate area of the shaded region? 2 of 11 11/25/09 2:59 PM

3 A cm B cm C cm D cm 5. If W = 6 cm, H = 3 cm, and L = 18 cm, what is the surface area of the prism? A cm B cm C cm D cm 6. The area of a triangle equals 96 units, and its base equals 12 units. What is the triangle's height? A. 20 units B. 13 units C. 16 units D. 9 units 7. The perimeter of a rectangle equals 284 units, and its length equals 65 units. What is the width of the rectangle? A. 84 units B. 154 units C. 77 units D. 207 units 3 of 11 11/25/09 2:59 PM

4 8. What is the approximate area of the figure above? A. 14 B. 8 C /2 D What is the approximate area of the figure above? A. 11 B. 7 C. 9 D of 11 11/25/09 2:59 PM

5 10. What is the approximate perimeter of the figure above if X = 18 in and Y = 15 in? A in B. 74 in C in D in 5 of 11 11/25/09 2:59 PM

6 Answers 1. C 2. A 3. D 4. D 5. C 6. C 7. C 8. A 9. A 10. D 6 of 11 11/25/09 2:59 PM

7 Explanations 1. The formula for the surface area of a cylinder is 2 r rh. The cylinder has a radius of R = 3 inches and height of H = 8 inches. Substitute the values into the surface area formula. 2 r rh = 2 (3 in.) (3 in.)(8 in.) = 18 in in. 2 = 66 in. 2 = in The volume of a cylinder is base height. Since the base is a circle, we need to find the area of a circle with radius R = 3. The area of a circle is R 2. So, the area of the base is 9 in 2. Now multiply the area of the base by the height of the cylinder. Volume = 9 in 2 8 in = 72 in 3 = in 3 3. Think of the sides of the square as the hypotenuse of a right triangle with legs that are 4 centimeters long. Each side is just a little less than 6 centimeters long. So, round the side lengths to 6 7 of 11 11/25/09 2:59 PM

8 centimeters. Given this, add the estimated lengths of the sides together to find the perimeter. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm 4. To find the area of the shaded region, find the area of the smaller circle and subract that from the area of the larger circle. Area of the smaller circle = r 2 = 4 cm cm 2 Next, find the radius of the larger circle using Pythagorean Theorem. Diameter = r + r 2 + r 2 ) = r + 2r 2 ) = r + r 2) = [1+ 2)] r = [1 + 2)] 2 cm 4.8 cm Radius 2.4 cm Now, use radius of the larger circle to find the area of the larger circle. Area of larger circle = (2.4) 2 cm cm 2 Finally, subtract the area of the smaller circle from the area of the larger circle. = 18.1 cm cm cm 2 8 of 11 11/25/09 2:59 PM

9 Area of the shaded region 5.5 cm 2 5. Since the base is a triangle, find the area of a triangle with a base of W = 6 cm and height of H = 3 cm. The formula for the area of a triangle is 1 / 2 bh. 1 /2 bh = 1 / 2 (6 cm)(3 cm) = 9 cm 2 So, the area of the base is 9 cm 2. Since the triangle that makes up the base is equilateral, all rectangular sides of the prism will have the same area. The formula for the area of the side is lw. lw = (6 cm)(18 cm) = 108 cm 2 To find the total surface area, add the areas of the individual sections together. There are 2 bases and 3 side rectangles. Surface Area = 2(area of the base) + 3(area of the side) = 2(9 cm 2 ) + 3(108 cm 2 ) = 18 cm cm 2 = 342 cm 2 6. The area of a triangle is equal to 1 / 2 Bh (B=base, h=height). You are given an area of 96 units. You are told that the base of the triangle is 12 units. 1 /2 Bh = 96 units 1 /2 (12) h = 96 units h = (2 96) / 12 h = 16 units Therefore, the height of the triangle equals 16 units. 7. The problem says the perimeter is 284 units and the length of the rectangle is 65 units. Therefore, two sides equal 130 units because: 9 of 11 11/25/09 2:59 PM

10 = 130. Next, subtract 130 from the perimeter to determine the total of the other two sides = 154. Finally, divide 154 by 2 to determine the rectangle's width = 77 units 8. The objects cover 8 full squares, 4 almost full squares, 2 half squares, and 6 almost empty squares. So, the figure's area covers about 14 squares, because = The figure covers 5 whole squares, 4 almost whole squares, 4 almost half squares, and 2 almost empty squares. So, the figure's area covers about 11 squares, because = To find the perimeter of the object above, find the circumference of the half-circle and then add this length to two times the hypotenuse of the right triangles. Circumference of Half-Circle = 1 / 2 ( D) = 1 / ( 2 18 in) = in 28.3 in Hypotenuse = 81 in in 2 ) = 306 in 2 ) in 17.5 in Perimeter = Circum. of half-circle + 2 Hypotenuse 28.3 in + 2 (17.5 in) 28.3 in + 35 in 10 of 11 11/25/09 2:59 PM

11 63.3 in Copyright 2009 Study Island - All rights reserved. 11 of 11 11/25/09 2:59 PM

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