radtad said:The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid?
How come the answer isn't just the intgegral from 0-8 of 1/2pi(4-x/2)^2
The formula for finding the volume of a solid with semicircular cross sections in the 1st quadrant is V = πr^2h, where r is the radius of the semicircle and h is the height of the solid.
The radius of the semicircle can be determined by finding the distance from the center of the semicircle to the edge. The height of the solid can be determined by finding the difference between the highest point of the semicircle and the x-axis.
No, the volume of a solid cannot be negative as it represents the amount of space occupied by the solid. If the radius or height values used in the formula result in a negative number, it means the solid does not exist.
As the radius and height values are directly proportional to the volume, increasing or decreasing these values will result in a corresponding increase or decrease in the volume of the solid. This is because a larger radius or height will result in a larger semicircular cross section, leading to a larger volume.
No, there is no limit to the number of semicircular cross sections that can be used to find the volume of a solid in the 1st quadrant. The more cross sections that are used, the more accurate the volume calculation will be.