Question :
271) A rectangular box with square base and no top : 1757208
271) A rectangular box with square base and no top is to have a volume of 32 ft3. What is the least amount of material required?
A) 42 ft2 B) 48 ft2 C) 40 ft2 D) 36 ft2
272) A rectangle with sides parallel to the axes is inscribed in the region bounded by the axes and the line x + 2y = 2. Find the maximum area of this rectangle.
A) 1/4 B) 2/3 C) 1/2 D) 1/3
273) Find the point on the plane x + 2y - z = 12 that is nearest the origin.
A) (4, 4, 0) B) (2, 4, 0) C) (-2, 8, 2) D) (2, 4, -2)
274) Find the distance from the point (1, -1, 2) to the plane x + y - z = 3.
275) Find the point on the sphere x2 + y2 + z2 = 4 that is closest to the point (3, 1, -1).
276) Find the point on the sphere x2 + y2 + z2 = 4 that is farthest from the point (3, 1, -1).
277) A rectangular box is to be inscribed inside the ellipsoid 2x2 + y2 + 4z2 = 12. Find the largest possible volume for the box.
A) 15 2 B) 12 2 C) 18 2 D) 16 2
