1 Geometry • Solid Geometry Revolving a circular area of radius R through 360 degrees about the x-axis generates a complete torus. The distance between the centre of the circle and the x-axis is d. The surface area of the torus is: Revolving a circular area of radius R through 360 degrees about the x-axis generates a complete torus. The distance between the centre of the circle and the x-axis is d. The surface area of the torus is: सेव करें Save सेव्ड Saved A. 3pi^2Rd 3pi^2Rd B. 4pi^2Rd 4pi^2Rd C. pi^2Rd pi^2Rd D. 2pi^2Rd 2pi^2Rd उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: B Correct Answer: B By Pappus' centroid theorem, surface area = circumference of the generating circle x distance travelled by its centroid = 2pi R x 2pi d = 4pi^2Rd. By Pappus' centroid theorem, surface area = circumference of the generating circle x distance travelled by its centroid = 2pi R x 2pi d = 4pi^2Rd.
2 Geometry • Solid Geometry Find the volume of the solid bounded by the ellipsoid x^2/4 + y^2/9 + z^2/49 = 1. Find the volume of the solid bounded by the ellipsoid x^2/4 + y^2/9 + z^2/49 = 1. सेव करें Save सेव्ड Saved A. 124 124 B. 176 176 C. 248 248 D. 312 312 उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: B Correct Answer: B The semiaxes are 2, 3 and 7. Thus volume = (4/3)pi(2)(3)(7) = 56pi, approximately 176. The semiaxes are 2, 3 and 7. Thus volume = (4/3)pi(2)(3)(7) = 56pi, approximately 176.