Final Exam Solid

Solid Mensuration Final Exam Sphere 1. The volume of a sphere in m3 is equal numerically to its surface area in m2. Find its radius m. R=3 2. What is the volume of the sphere whose surface area is 108 sq.m.? 105.5 cu.cm. 3. What is the surface area of a sphere whose volume is 36 cu.cm? 52.7 sq. cm 4. What is the ratio of the volume of a sphere in m3 to its surface area in m2, if the diameter is 12m? Ratio is 2:1 5. The volume of a sphere in cm3 is equal to twice its surface area in cm2. Find it radius in cm. R = 6cm 6. The ratio of the volume of a sphere to its surface area is 2.56258. Find its volume in cu.m. V = 1903.20m3 7. By how much (percent) is the volume of a sphere reduced if the radius is reduced by 25%. V is reduced by 57.8% 8. A spherical steel ball having a radius of 10 cm is placed into a circular cylinder containing water. If the radius of the cylinder is 12 cm, by how much will the water level rise? 9.26cm 9. The ratio of the surface area of sphere A to the surface area of sphere B is 4. The ratio of the volume of sphere B to the volume of Sphere C is 3. Find the ratio of the volume of sphere A to the volume of sphere C. Va/Vc = 24 Find the volume of a spherical cone in a sphere of radius 17 cm in the radius of its zone is 8 cm. (C) a.2120.35 b. 1426.34 c. 1210.56 d. 2316.75 If the surface areas of two spheres are 24 cm2 and 96 cm2 respectively. Find the ratio of their volume. (C) a.1/4 b. 5 c. 1/8 d. 3/5 Spherical Segment 10. The level of gasoline in a spherical tank, 6m in diameter, dropped from 5.5 m to 3.5. How much gasoline was taken out? 40.3m3 11. A sphere has a diameter of 30 cm. The altitude of the first segment is 6cm. What is the ratio of area of zone of the 2nd segment to that of the first? 4:1

12. A spherical container with a radius of 2m was holding water at a depth of 1.5m. How many cu.m. of water were consumed if the depth now is only 0.25m? 10.2m3 13. What is the area in sq.m. of the zone of a spherical segment having a volume of 1470.265 cu.m. if the diameter of the sphere is 30m? 565.487m2 14. A spherical tank 4m in diameter contains 5.236 cu.cm of water. Find the height of the water surface from the bottom. H = 1cm Spherical Zone 15. A spherical segment has 2 parallel bases. The bigger base is a great circle with a radius of 80 cm. The smaller base has a radius of 30cm. Find the area of the zone in sq. cm. 37278 sq.cm 16. The parallel bases of a spherical segment have diameters of 40 cm and 25 cm. The radius of the great circle is 20 cm. What is the area of the zone in cm2? 1962sq. cm. 17. One meter curved strip around and above the base of a hemispherical dome is to be painted with 2 coats of enamel which has a spreading capacity of 200 sq.ft. per gallon. Determine the number of gallons of paint needed if the diameter of the dome is 16m. 5.39 gallons Spherical Sector 18. A spherical sector is cut from a sphere whose radius is 12cm. Find its volume if its central angle is 30deg. 123.3cu cm. 19. A spherical sector is cut from a sphere whose radius is 12cm. Find its volume if its central angle is 20deg. 55cu cm. 20. A spherical sector is cut from a sphere such that its central angle is 25 deg and its volume is 185 cu cm. Determine the radius of the sphere. 15.50cm 21. A spherical sector is cut from a sphere such that its central angle is 25 deg and its volume is 216 cu cm. Determine the radius of the sphere. 16.3cm 22. A sphere is whittled down into a spherical sector with a central angle of 53deg and a volume of 420 cu cm. What is the radius of the sphere? 12.4cm Theorem of pappus 23. The volume generated by rotating the curve 9x2 + 4y2 = 36 about the line 4x + 3y = 20 is (D) a. 48pi b. 58pi c. 42pi

d. 48pi 24. Find the volume generated by revolving the area bounded by the ellipse y2/9 +x2/4 = 1 about the line x = 3 (B) a. 347.23 cu. units b. 355.31 cu. units c. 378.43 cu. units d. 389.51 cu. units 25. The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated? (B) a. 2218.6 b. 2228.8 c. 2233.4 d. 2208.5 26.