tailieunhanh - SAT II Math Episode 1 Part 4

Tham khảo tài liệu 'sat ii math episode 1 part 4', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Math Review Illustrative Problems and Solutions 55 Solution 4. Point O is the center of both circles. If the area of shaded region is 9 n and OB 5 find the radius of the unshaded region. Let OA r. Then 25 7Ĩ - 7ĨT1 9 r 25-r2 9 r2 16 r 4 5. Given rectangle ABCD semicircles O and P with diameters of 8. If CD 25 what is the area of the shaded region Solution D 25 c Area of rectangle 25 8 200 Area of both semicircles n r2 16 n Area of shaded region 200 - 16 n 6. Find the ratio of the area of a circle inscribed in a square to the area of the circle circumscribed about the square. Solution Let the side of the square be s. Then the radius of the inscribed circle is . Since OTP is right isosceles the radius OP of the circumscribed circle is Area of inner circle ĩt Area of outer circle ns1 1 Ratio - ĩ- 1 4 2 T 2 ARCO SAT II Math arco 56 Part III 7. A square is inscribed in a circle. What is the ratio of the area of the square to that of the circle Solution In the figure let OP OQ 1 In right OPQ PQ 4Ĩ Area of square PQ1 5 2 j 2 Area of circle 7r l 2 ĨĨ 2 Ratio 7Ĩ SOLID FIGURES 1. If the radius of a right circular cylinder is tripled what must be done to the altitude to keep the volume the same Solution V nr2h Tripling r has the effect of mutiplying V by 9. To keep the volume constant h has to be divided by 9. 2. The surface area of a sphere is 100 sq in. What is the surface area of a sphere having a radius twice the radius of the given sphere Solution Since S 4nr2 100 s J s r 2 _f2V _4 too- r Id - 1 S 400 3. The ratio of the diagonal of a cube to the diagonal of a face of the cube is A 2 5 3 B 3 6 C 3 V2 D 73 1 E 76 3 Solution B Let each side of cube equal 1. diagonal of cube D Vl2 12 12 5 3 diagonal of face D Vl2 12 5 2 T3 7Ĩ - 3 D 5 2 5 3-76 arco ARCO SAT II Math Math Review Illustrative Problems and Solutions 57 Solution Solution 4. A pyramid is cut by a plane parallel to its base at a distance from the base equal to two-thirds the .