# Sphere

## 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 *V*_{sphere} = 4/3 π*r*^{3} as a function of *x* (radius), and *x* (radius) as a function of *t* (time).

A. V(t) = 5/2 πt^{3} |
C. V(t) = 9/2 πt^{3} |

B. V(t) = 7/2 πt^{3} |
D. V(t) = 3/2 πt^{3} |

## A solid spherical ball remolded into a hollow spherical ball

**Problem**

A 523.6 cm^{3} 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 |

## 033 Review Problem - Finding which one is the better bargain

**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.

## 015 Review Problem - Volume of spherical shell

**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.

## 003 Review Problem - Sphere melted into cylinder

**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.

## 016 Radius of the sphere circumscribing a regular triangular pyramid

**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.

## 015 Two unequal balls inside the cylinder

**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.

## 013 Insciribed and circumscribed sphere about a cube - volume comparison

**Example 013**

Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.

## 012 Sphere circumscribed about a right circular cylinder

**Example 012**

Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.