1. use the Angle Bisector Theorem.
2. The volume of oil is the area of a circular cap times the length. So, the the formula for the area of a circular cap. Then if the oil volume is v, the depth would have been (v/60π)*15
3. Consider the problem in 2D, and draw a rectangle. If the rectangle has width x and height y, the area in question is the rectangle plus 4 strips of width 1 on each side, plus 4 quarter-circles of radius 1 at the corners. That is xy + 2x+2y + π
Now extend that to 3D and the volume will be the brick, plus 6 blocks on the faces, of thickness 1, plus a complete sphere of radius 1:
3*4*5 + 2(3*4+4*5+3*5) + 4π/3
= (462+4π)/3
1. The sides of triangle CAB are in the ratio of 2:3:4. Segment BD is the angle bisector drawn to the shortest side, dividing it into segments AD and DC. What is the length, in inches, of the longer subsegment of side AC if the length of side AC is 10 inches? Express your answer as a common fraction.
2. A right cylindrical oil tank is 15 feet tall and its circular bases have diameters of 4 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 3 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.
3. Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures 3 by 4 by 5 units. Given that the volume of this set is {m+n\pi}/p, where m, n, and p are positive integers, and n and p are relatively prime, find m+n+p.
2 answers
that is incorrect.
1 answer