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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Answer the given questions about the indicated examples of this section.In Example 3, if h is halved, what is the volume?Data from Example 3A grain storage building is in the shape of a cylinder
Determine each of the following as being either true or false. If it is false, explain why.A quadrilateral with two sides of length a and two sides of length b is always a parallelogram.
Find the area of a triangular wall pennant of sides 24.6 cm, 36.5 cm, and 40.7 cm.
Refer to the circle with center at O in Fig. 2.85. Identify the following.(a) A secant line(b) A tangent line A B E Fig. 2.85 0 C D
An office building hallway floor is designed in the trapezoidal shape shown in Fig. 2.147. What is the area of the hallway? 3.12 m 4.70 m 2.76 m 9.96 m Fig. 2.147 4.70 m
Determine ∠A in the indicated figures.Fig. 2.40 (a) A с 84° (a) 40° B
Determine each of the following as being either true or false. If it is false, explain why.The circumference of a circle of diameter d is πd.
Identify the indicated angles and sides in Fig. 2.10.Two acute angles A. E B Fig. 2.10 D C
What is the diagonal distance between corners of a rectangular field 125 ft wide and 170 ft long?
Answer the given questions related to Fig. 2.106.If the trapezoidal rule was used to find the area of the region in Fig. 2.106, would the answer be approximate or exact? Explain. Fig.
Find the volume or area of each solid figure for the given values. Volume of cube: e = 6.95 ft
Find the perimeter of each figure.Square: side of 85 m
Determine each of the following as being either true or false. If it is false, explain why.Simpson’s rule could be used to find the approximate area in Example 2 of Section 2.5.
Find the volume or area of each solid figure for the given values. Volume of right circular cylinder: r = 23.5 cm, h = 48.4 cm
Refer to the circle with center at O in Fig. 2.85. Identify the following.(a) Two chords(b) An inscribed angle A B E Fig. 2.85 0 C D
Answer the given questions related to Fig. 2.106.Explain why Simpson’s rule cannot be used to find the area of the region in Fig. 2.106. i I I I I I I I I I I I I I I I I 1 I 1 I Fig. 2.106
Determine ∠A in the indicated figures.Fig. 2.40 (b) B 48° с (b) A
Identify the indicated angles and sides in Fig. 2.10.Two right anglesFigure 2.10 A- E B D -C
Find the perimeter of each figure.Rhombus: side of 2.46 ft
Determine each of the following as being either true or false. If it is false, explain why.The volume of a right circular cylinder is the base area times the height.
What is (a) The mass (in kg) of a cubical block of ice, the edge of which is 0.40 m (the density of ice is 0.92 × 103kgm3),(b) The surface area of the block?
Refer to Fig. 2.87. Determine the indicated arcs and angles.∠ABCFig.2.87 80° A C 60° B
Find the third side of the right triangle shown in Fig. 2.42 for the given values.a = 175 cm, c = 551 cm C b Fig. 2.42 a
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠BDF A AF || BE D 44° B Fig.
Find the third side of the right triangle shown in Fig. 2.42 for the given values.b = 0.474 in., c = 0.836 in. C b Fig. 2.42 a
Refer to Fig. 2.87. Determine the indicated arcs and angles.∠ACBFig.2.87 80° A C 60° B
Find the perimeter or area of the indicated figure.Area: circle, d = 0.328 m
Solve the given problems.The base area of a cone is one-fourth of the total area. Find the ratio of the radius to the slant height.
Solve the given problems.What conclusion can you make about the two triangles formed by the sides and diagonal of a parallelogram? Explain
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠ABE A AF || BE D 44° B Fig.
Use the right triangle in Fig. 2.43.Find ∠B. 23° с 90.5 cm B 38.4 cm Fig. 2.43
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠DEB A AF || BE D 44° B Fig.
Find the volume of the indicated solid geometric figure.Prism: base is right triangle with legs 26.0 cm and 34.0 cm, height is 14.0 cm
Solve the given problems.In designing a spherical weather balloon, it is decided to double the diameter of the balloon so that it can carry a heavier instrument load. What is the ratio of the final
Solve the given problems.Find the area of a square whose diagonal is 24.0 cm.
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠DBE A AF || BE D 44° B Fig.
Change the given angles to radian measure.22.5°
Use the right triangle in Fig. 2.43.Find side c. 23° с 90.5 cm B 38.4 cm Fig. 2.43
Find the volume of the indicated solid geometric figure.Cylinder: base radius 36.0 in., height 2.40 in
Solve the given problems.During a rainfall of 1.00 in., what weight of water falls on an area of 1.00 mi2? Each cubic foot of water weighs 62.4 lb.
Solve the given problems.In a trapezoid, find the angle between the bisectors of the two angles formed by the bases and one nonparallel side.
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠DFE A AF || BE D 44° B Fig.
Solve the given problems.Noting the quadrilateral in Fig. 2.67, determine the sum of the interior angles of a quadrilateral.Fig. 2.67 T 1 I
Change the given angles to radian measure.60.0°
Find the volume of the indicated solid geometric figure.Pyramid: base area 3850ft 2 , height 125 ft
Solve the given problems.A rectangular box is to be used to store radioactive materials. The inside of the box is 12.0 in. long, 9.50 in. wide, and 8.75 in. deep. What is the area of sheet lead that
Change the given angles to radian measure.125.2°
Use the right triangle in Fig. 2.43.Find the area. 23⁰ C 90.5 cm B 38.4 cm Fig. 2.43
Solve the given problems.Express the area A of the large rectangle in Fig. 2.68 formed by the smaller rectangles in two ways. What property of numbers is illustrated by the results? a b C Fig. 2.68
Solve the given problems.A swimming pool is 50.0 ft wide, 78.0 ft long, 3.50 ft deep at one end, and 8.75 ft deep at the other end. How many cubic feet of water can it hold? (The slope on the bottom
Find the measures of the angles in the truss shown in Fig. 2.14. A truss is a rigid support structure that is used in the construction of buildings and bridges.∠ADE A AF || BE D 44° B Fig.
Solve the given problems.The sum S of the measures of the interior angles of a polygon with n sides is S = 180(n − 2). (a) Solve for n. (b) If S = 3600°, how many sides does the polygon
Find the volume of the indicated solid geometric figure.Sphere: diameter 2.21 mm
Change the given angles to radian measure.323.0°
Find a formula for the indicated perimeter or area.The perimeter of the quarter-circle in Fig. 2.88. Fig. 2.88 r
Find the volume of the indicated solid geometric figure.Cone: base radius 32.4 cm, height 50.7 cm
Find the indicated distances between the straight irrigation ditches shown in Fig. 2.15. The vertical ditches are parallel.aFigure 2.15. 3.20 m 3.05 m C 4.75 m a 5.05 m 6.25 m b d
Solve the given problems.Express the area of the square in Fig. 2.69 in terms of the smaller rectangles into which it is divided. What algebraic expression is illustrated by the results? b a a b Fig.
Solve the given problems.The volume of a frustum of a pyramid is(This equation was discovered by the ancient Egyptians.) If the base of a statue is the frustum of a pyramid, find its volume if a =
Solve the given problems.What is the angle between the bisectors of the acute angles of a right triangle?
Solve the given problems.The Alaskan oil pipeline is 750 mi and long has a diameter of 4.0 ft. What is the maximum volume of the pipeline?
Find a formula for the indicated perimeter or area.The perimeter of the figure in Fig. 2.89. A quarter-circle is attached to a triangle.Fig. 2.89. b a r
Solve the given problems.Noting how a diagonal of a rhombus divides an interior angle, explain why the automobile jack in Fig. 2.70 is in the shape of a rhombus. Fig. 2.70
Find the volume of the indicated solid geometric figure.Frustum of a cone: base radius 2.336 ft, top radius 2.016 ft, height 4.890 ft
Find the indicated distances between the straight irrigation ditches shown in Fig. 2.15. The vertical ditches are parallel.bFigure 2.15. 3.20 m 3.05 m C 4.75 m a 5.05 m 6.25 m b d
Find a formula for the indicated perimeter or area.The perimeter of the segment of the quarter-circle in Fig. 2.88. Fig. 2.88 r
Solve the given problems.If the midpoints of the sides of an isosceles triangle are joined, another triangle is formed. What do you conclude about this inner triangle?
Find the indicated distances between the straight irrigation ditches shown in Fig. 2.15. The vertical ditches are parallel.cFigure 2.15. 3.20 m 3.05 m C 4.75 m a 5.05 m 6.25 m b d
Find the surface area of the indicated solid geometric figureTotal area of cube of edge 0.520 m
Find the indicated distances between the straight irrigation ditches shown in Fig. 2.15. The vertical ditches are parallel.dFigure 2.15. 3.20 m 3.05 m с 4.75 m a 5.05 m 6.25 m b d
Solve the given problems.For what type of triangle is the centroid the same as the intersection of altitudes and the intersection of angle bisectors?
Solve the given problems.Part of an electric circuit is wired in the configuration of a rhombus and one of its altitudes as shown in Fig. 2.71. What is the length of wire in this part of the circuit?
Find a formula for the indicated perimeter or area.The area of the figure in Fig. 2.89.Fig. 2.89. b a r
Solve the given problems.A pole supporting a wind turbine is constructed of solid steel and is in the shape of a frustum of a cone. It measures 62.5 m high, and the diameter of the pole at the bottom
Find the surface area of the indicated solid geometric figureTotal area of cylinder: base diameter 12.0 ft, height 58.0 ft
Solve the given problems.Is it possible that the altitudes of a triangle meet, when extended, outside the triangle? Explain.
Solve the given problems.A glass prism used in the study of optics has a right triangular base. The legs of the triangle are 3.00 cm and 4.00 cm. The prism is 8.50 cm high. What is the total surface
Solve the given problems.The Great Pyramid of Egypt has a square base approximately 250yd on a side. The height of the pyramid is about 160 yd. What is its volume? See Fig. 2.125. Fig. 2.125 160 yd
Find the surface area of the indicated solid geometric figureLateral area of cone: base radius 2.56 in., height 12.3 in.
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.25°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Solve the given problems.The altitude to the hypotenuse of a right triangle divides the triangle into two smaller triangles. What do you conclude about the original triangle and the two new
Solve the given problems.A walkway 3.0 m wide is constructed along the outside edge of a square courtyard. If the perimeter of the courtyard is 320 m,(a) what is the perimeter of the square formed by
Solve the given problems.The measure of on a circle of radius r is 45°. What is the length of the arc in terms of r and π? AB
Solve the given problems.Describe the location of the midpoints of a set of parallel chords of a circle.
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.45°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Solve the given problems.If two triangles have the same three angles, can you conclude that the triangles are congruent? Explain why or why not.
Solve the given problems.In Fig. 2.44, show that △MKL ~ △MNO. L K M Fig. 2.44 N 0
Find the surface area of the indicated solid geometric figureTotal area of sphere: d = 12,760 km
Solve the given problems.A paper cup is in the shape of a cone as shown in Fig. 2.126. What is the surface area of the cup? 3.60 in. T 1 I Fig. 2.126 3.50 in.
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.65°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Use Fig. 2.133. Line CT is tangent to the circle with center at O. Find the indicated angles.∠BTAFig. 2.133 T C B Э A 0 50°
Solve the given problems.An architect designs a rectangular window such that the width of the window is 18 in. less than the height. If the perimeter of the window is 180 in., what are its dimensions?
Use Fig. 2.133. Line CT is tangent to the circle with center at O. Find the indicated angles.∠TABFig. 2.133 T C B Э A 0 50°
Solve the given problems.Find the area of the cross section of concrete highway support shown in Fig. 2.72. All measurements are in feet and are exact.Fig. 2.72.
Solve the given problems.Spaceship Earth (shown in Fig. 2.127) at Epcot Center in Florida is a sphere of 165 ft in diameter. What is the volume of Spaceship Earth? Fig. 2.127 165 ft
Solve the given problems.A beam support in a building is in the shape of a parallelogram, as shown in Fig. 2.73. Find the area of the side of the beam shown. ! 1.80 ft 3.93 ft Fig. 2.73
Solve the given problems.A propane tank is constructed in the shape of a cylinder with a hemisphere at each end, as shown in Fig. 2.128. Find the volume of the tank. 1 | 1 1 -6.50 ft- Fig.
Solve the given problems.In Fig. 2.45, show that △ACB ~ △ADC. В с D Fig. 2.45 A
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.70°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Solve the given problems.In Fig. 2.90, chords AB and DE are parallel. What is the relation between △ABC and △CDE? Explain. A D C Fig. 2.90 E B

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