33. Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r. Answer 34. If the two equal sides of an isosceles triangle have length a, find the length of the third side that maximizes the area of the triangle. 35. If one side of a triangle has length a and another has length 2a, show that the largest possible area of the triangle is a². 36. A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4-2². What is the largest possible area of the rectangle? 37. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder. Answer 38. A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest ossible volume of such a cylinder. 39. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface area of such a cylinder.

33. Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r. Answer 34. If the two equal sides of an isosceles triangle have length a, find the length of the third side that maximizes the area of the triangle. 35. If one side of a triangle has length a and another has length 2a, show that the largest possible area of the triangle is a². 36. A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4-2². What is the largest possible area of the rectangle? 37. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder. Answer 38. A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest ossible volume of such a cylinder. 39. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface area of such a cylinder.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter3: Triangles

Section3.CT: Test

Problem 19CT: The perimeter of an isosceles triangle is 32cm. If the length of the altitude drawn to the base is...

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