net square cubic rectangular prism surface area cylinder 1. The sum of all areas of lateral faces and bases of a solid figure is called __________. 2. The flat pattern that you can fold to form a solid figure is known as __________. 3. The sum of the areas of its six faces is the surface area of a __________. The area of each face is equal to the product of length and width. 4. The sum of the areas of the two circular bases and rectangular lateral area is the surface area of the __________. 5. To measure surface area, we use __________ units.
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Measurement and Geometry Section A: Quiz for Lessons Through Choose the best answer. 1. Find the volume of the figure below. a) 43.9 cm^3 b) 44 cm^3 c) 43.96 cm^3 2. Find the circumference of the circle to the nearest tenth. Use 3.14 for ̀́. a) 37.68 cm b) 37.7 cm c) 37.6 cm d) 38 cm 3. Find the area of the circle with a diameter of 8 units. Round to the nearest tenth. Use 3.14 for ̀́. a) 21 cm^2 b) 791.3 cm^2 c) 1017 cm^2 d) 2373.8 cm^2 4. A rainwater collection tank is shaped like a cylinder with a diameter and height of 6 ft. What is its volume? Use 3.14 for ̀́. a) 150.7 ft^3 b) 754 ft^3 c) 301.4 ft^3 5. To the nearest tenth, find the area of a circle with a radius of 3 units. Use 3.14 for ̀́. a) 28.3 cm^2 b) 18.8 cm^2 c) 113.0 cm^2 6. Find the volume of a rectangular prism with a base of 15 units by 30 units and a height of 20 units. a) 62 units^3 7. A juice box measures 4 in. by 3 in. by 5 in. Explain whether changing the 4 in to 10 in will double the amount of juice the box holds. a) Yes, Volume 120 in^3 8. Solve the equation: 195 > 195/6?
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It follows from Theorem 140 that all n of the angle bisectors of a regular n-gon intersect at the same point. We call this point the center of the regular n-gon. (Figure 7.4.) Theorem 141. The segments connecting the center of a regular n-gon to its vertices partition it into n congruent isosceles triangles. Corollary 142. The vertices of a regular n-gon are all the same distance from its center. Recall that the distance from a point to a line is the length of the perpendicular segment connecting them. Corollary 143. The sides of a regular n-gon are all the same distance from its center. The perpendicular distance r from the center of a regular n-gon to one of its sides is called its apothem. Each of the regular n-gons in Figure 7.3 has the same apothem. Imagine that you tie a string around the center of the regular n-gon in Figure 7.4, walk to the vertex P, and travel clockwise around the n-gon and back to P. The string will then pass through four right angles, a total of 4 × 90° = 360°. This tells us that the n congruent central angles have degree measure adding up to 360°. Consequently each central angle measures (360/n)°. Problem 144. Find the perimeter and the area of an equilateral triangle with apothem r. In Problem 19 you constructed and equilateral triangle, and in Problem 58 you constructed a square. Problem 145. Construct a regular hexagon. If its apothem is r, what is its perimeter and its area? Problem 146. Construct a regular octagon. If its apothem is r, what is its perimeter and its area? Problem 147. Construct a regular 16-gon. Problem 148. Describe, without doing it, how you would construct a regular 2^{50}-gon. (Note that 4 = 2^2, that 8 = 2^3 and that 16 = 2^4.) We can now apply these ideas to measure the circumference and area of a circle. Our strategy will be to measure the perimeter and area of a regular n-gon whose center is the center of the circle and whose apothem r is the radius of the circle. We say that this circle is inscribed in the regular n-gon. In Figure 7.5 we see that the perimeter
Find the surface area of each of the following polyhedrons. (See the shapes on page 544 ) Give exact answers. a. A regular tetrahedron with an edge $4 \mathrm{cm}$ b. A regular hexahedron with an cdge $4 \mathrm{cm}$ c. A regular icosahedron with an edge $4 \mathrm{cm}$ d. The dodecahedron shown at right, made of four congruent rectangles and eight congruent triangles (GRAPH CANT COPY)
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