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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
4.7-Number 36, please.
Transcribed Image Text: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.
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