Topic 4: Plane and Solid Geometry
1. Deals Deals with the propert properties ies of plane plane figures figures or geometric geometrical al shapes shapes of two – dimensions. A Plan Plane e Geom Geomet etry ry C Eucl Euclid idea ean n Geom Geomet etry ry B Solid Geometry D Projective Geometry 2. Deals Deals with the study study of those those properties properties of plane plane figures figures that that re unchanged unchanged when when a set of points is projected onto a second plane. A Plan Plane e Geom Geomet etry ry C Eucl Euclid idea ean n Geom Geomet etry ry B Solid Geometry D Projective Geometry 3. Two angl angle e with with a common common leg leg is cal called led A Adja Adjace cent nt angl angles es B Complementary Angles
C Supp Supple leme ment ntar ary y Angl Angles es D Vertical Angles
4. Are angle angles s formed formed by by two intersect intersecting ing lines lines.. A Adja Adjace cent nt angl angles es C Supp Supple leme ment ntar ary y Angl Angles es B Complementary Angles D Vertical Angles 5. A _______ is a straight straight line line which divide divides s a geometric geometric figure into into two equal figures figures.. A Reciprocal C Bisector B Expl Explem emen enta tary ry Angl Angles es D Co Conj njug ugat ate e 6. The area area bounded bounded by a chord of a parabol parabola a that is perpend perpendicul icular ar to its axis axis and the curve, cut off by the chord. A Spherical segment C Parabolic sector B Sphe Spheri rica call sect sector or D Para Parabo boli lic c segm segmen entt 7. If a regula regularr polygon polygon has 27 diagona diagonals, ls, then then it is is a, A Nonagon C Hexagon B Pe Pentagon D He Heptagon 8. One One angl angle e is 200 less than thrice its supplement. What are the angles? A 200, 1600 C 550, 1250 B 450, 1350 D 500, 1300 9. A regular regular octagon octagon is inscribe inscribed d in a circle circle of radius radius 10. Find the the area of the octagon. A 228.2 C 238.2 B 288.2 D 282.8 10. A piece of wire is shaped to enclose a square whose area is 169 sq. cm. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is __________. A 165 sq. cm. C 175 sq. cm. B 156 sq. cm. D 17 1 70 sq. cm. 11. Find the area of the parallelogram whose sides sides are 67 cm and 43 cm, the acute angle between them being 65 0. A 1305 cm2 C 1805 cm2 B 1611 cm2 D 2611 cm2 12. Given a triangle, triangle, C = 100 0, a = 15 m, b = 20 m. Find c. A 26 m C 28 m B 27 m D 29 m 13. One side of a rectangle inscribed in a circle of radius 8.5 cm, is 8 cm. Find the area of the rectangle. A 120 cm2 C 150 cm2 B 135 cm2 D 160 cm2
plane & solid geometry / page 2
14. The two bases of a trapezoid are 12 inches and 18 inches respectively. If the angles at the extremities of one base are 65 0 and 400 respectively, find the longer leg. A 5.63 in C 7.21 in B 6.23 in D 7.81 in 15. The area of the circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m.? A 100.25 C 104.25 B 102.25 D 105.25 16. The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. The area of the largest circle is A 72 pi C 64 pi B 32 pi D 61 pi 17. The area of a regular hexagon inscribed in a circle of radius 1 is A 1.316 C 2.598 B 2.945 D 3.816 18. A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon. A 36.45 sq. cm. C 45.63 sq. cm. B 63.54 sq. cm. D 54.36 sq. cm. 19. Determine the area of a regular 6 – star polygon if the inner regular hexagon has 10 cm. sides. A 441.67 cm2 C 519.60 cm2 B 467.64 cm2 D 493.62 cm2 20. A copying machine reduces the side of a triangle by 20%. The area of the triangle is reduced by A 26% C 20% B 36% D 30% 21. A spherical balloon is being inflated so that the surface area increases by 20%, then the volume of the sphere increases by A 20% C 31.5% B 30% D 31.45% 22. If the edge of the cube is increased by 20%, by how much will the surface area increase? A 24% C 42% B 40% D 44% 23. Given a sphere of diameter d, what is the percentage increase in volume when the surface area is increased by 21%? A 10% C 30% B 21% D 33% 24. The diameters of the spheres are in the ratio 2:3 and the sum of their volumes is 1260 cubic meter. Find the volume of the larger sphere. A 882 m2 C 950 m2 B 910 m2 D 972 m2 25. The three dimensions of a rectangular parallelepiped are in the ratio 2:3:5. If the volume is 810 cu. cm., what is the length of the longest side? A 6 cm C 15 cm B 18 cm D 9 cm
plane & solid geometry / page 3
26. Three spheres of radii 1, 2, and 3 inches, respectively, are melted and formed into a new sphere. Find the radius of this new sphere. A 3.3 C 5.3 B 4.3 D 6.3 27. What is the volume of the frustum of a cone whose upper base is 15 cm in diameter and the lower base 10 cm in diameter with an altitude of 25 cm? A 3018.87 cm3 C 3108.87 cm3 B 3180.87 cm3 D 3081.87 cm3 28. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 cu. m. Find its altitude in meters. A 3.25 C 3.75 B 3.50 D 4.00 29. Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At this moment, how deep is the water in the bigger tank? The bigger tank is has a diameter of 6 ft and a height of 10 ft, the smaller tank has a diameter of 6 ft and a height of 8 ft. Neglect the water in the pipeline. A C B D 30. A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled with water. All 8 marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are of the same size. What is the volume of water in the container? A 0.38 in3 C 3.8 in3 B 2.5 in3 D 4.2 in3
