Find the radii of the bases and the height of the truncated cone knowing that its axial section

| May 28, 2021 | education

Find the radii of the bases and the height of the truncated cone knowing that its axial section is limited to a quadrangle with sides of 12 cm 125 cm 125 cm 100 cm.

Since in the axial section of the truncated cone, an isosceles trapezoid is obtained, the bases of which are the diameters of the circles lying in the bases of the cone. Consider such an axial section ABCD. It is known from the problem statement that the axial section is bounded by a quadrangle with sides of 12 cm; 125 cm; 125 cm; 100 cm, then the generatrix AB = 125 cm; base AD = 100 cm; base BC = 12 cm; and the radii of the bases of the cone will be AD / 2 = 100/2 cm = 50 cm and BC / 2 = 12/2 cm = 6 cm. From the apex of the trapezoid, we will lower the height of the VC of the truncated cone. Consider a right-angled triangle ABK, find the leg VK according to the Pythagorean theorem: AB² = BK² + AK², where AK = (AD – BC): 2 = (100 – 12): 2 = 44 (cm). We get the equation: 100² = BK² + 44², BK = 117 cm.
Answer: 50 cm and 6 cm are the radii of the bases, 117 cm is the height of the truncated cone.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.