If the volume of the cone is reduced by 15% then 85% of its original volume remains . If its height is reduced by 5% , 95% of its original height remains .Use the formula for the volume of a cone , and let P be the proportion of the radius that remains ,
`0.85((1)/(3)pir^(2)h)=(1)/(3) pi (pr)^(2) (0.95h)`
This equation simplifies to 0.85 = `0.95p^(2) ,` so `p= 0.945`. Therefore , the radius must be reduced by 5.4 %
A solid figure can be obtained by rotating a plane figure some line in the plane that does not intersect the figure .
THe coordinate plane can be extended by adding a third axis , the z-axis , which is perpendicular to the other two . picture the corner of a room . The corner itself is the origin .The edages between the walls and the floor the x-and y-axes . The edge between the two walls is the z-axis . The first octant of this three - dimensional coordinate system and the point (1,2,3) are illustrated below.
A point that has zero as any coordinate must lie on the plane formed by the other two axes . If two coordinates of a point are zero , then the point lies on the nonzero axis .The three - dimensional pythagorean yields a formula for the distance between two points `(x_(1),y_(1),z_(1))`
and `(x_(2),y_(2),z_(2))` in space .
`d=sqrt( (x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2))`
A three - dimensional coordinate system can be used to graph the variable z as a function of the two variables x and y , but such graphs are beyond the scope of the Level 2 Test.
