Equation of the sphere of radius 3 and tangent to coordinate-planes

Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.

A.   x2+y2+z29=0
B.   x2+y2+z26x6y6z+18=0
C.   x2+y2+z24x4y4z+12=0
D.   x2+y2+z28x8y8z+14=0

 

Volume of Inflating Spherical Balloon as a Function of Time

Problem
A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume V of the balloon as a function of time t (in seconds). Hint: Use composite function relationship Vsphere = 4/3 πr3 as a function of x (radius), and x (radius) as a function of t (time).

A.   V(t) = 5/2 πt3 C.   V(t) = 9/2 πt3
B.   V(t) = 7/2 πt3 D.   V(t) = 3/2 πt3