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. $x^2 + y^2 + z^2 - 9 = 0$ |
| B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |
| C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |
| D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |
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 |
Problem
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
| A. 1.3 cm | C. 1.2 cm |
| B. 1.5 cm | D. 1.6 cm |
The inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?
Problem 33
Disregarding quality, and considering oranges as spheres, determine which is the better bargain, oranges 2-3/4 in. in diameter at 15 cents per dozen, or oranges averaging 3-1/2 in. in diameter at 30 cents per dozen.
Problem 15
A spherical shell 2 in. thick has an outer diameter of 12 in. Find the volume of the material of which it is made.
Problem 3
Two spheres of lead, of radii 2 and 3 in., respectively, are melted into a cylinder of revolution of radius 1 in. Find the altitude of the cylinder.
Example 016
Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.
Example 015
Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them.
Example 013
Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.
