Geometry

Step 1: Relation between volume and surface area.
The volume and surface area of a sphere are given by the formulas: We are given that the rate of change of the volume is c.c./s and need to find when cm.
Step 2: Differentiating the volume equation.
Differentiating with respect to , we get: Substituting , we have: Step 3: Finding the rate of change of the surface area.
Now, differentiate with respect to : Substitute and : Step 4: Conclusion.
Thus, the rate of change of the surface area when the radius is 5 cm is .

Step 1: Understanding direction ratios.
The direction ratios of a line are given by the coefficients of and in the vector equation of the line. The equation of the line is: This represents the vector equation of a straight line in 3D space.
Step 2: Identifying the direction ratios.
The direction ratios are the coefficients of and in the second part of the equation, i.e., the direction ratios are .
Step 3: Conclusion.
Thus, the direction ratios of the straight line are .