SOLUTION: Find the volume in terms of pi of a sphere whose surface area is {{{36*pi^2}}}. The formula for the volume of a sphere is {{{ V=(4/3)*(pi)*r^3}}} and for the surface area of a sphe

SOLUTION: Find the volume in terms of pi of a sphere whose surface area is {{{36pi^2}}}. The formula for the volume of a sphere is {{{ V=(4/3)(pi)*r^3}}} and for the surface area of a sphe

Question 76989This question is from textbook PRENTICE HALL MATHEMATICS GEOMETRY
: Find the volume in terms of pi of a sphere whose surface area is . The formula for the volume of a sphere is and for the surface area of a sphere is This question is from textbook PRENTICE HALL MATHEMATICS GEOMETRY

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
I've taken the liberty of changing the problem a little to add the correct formula for the
Surface Area (call it S) of a sphere. This formula is
.
You are told that for a particular sphere, the surface area is . Substitute
this value into the surface area equation in place of S and you get:
.

.
What we are going to do now is solve this equation for r. Begin by dividing both sides of
the equation by 4. When you do that the equation reduces to:
.

.
Next divide both sides of the equation by . This further reduces the equation to:
.

.
Since we're going to solve for r, let's transpose the equation (switch left and right sides)
to get it into the more conventional form:
.

.
Now you can solve for r by taking the square root of both sides. When you do that you
get:
.

.
We now know what the radius of the given sphere is. To find the volume (V) of this sphere
we substitute this value for the radius into the volume equation. The volume equation is:
.

.
substitute for the radius in the volume equation and you get:
.

.
By the rules of exponents, when you cube a factored quantity, it is equivalent to cubing
each of the individual factors. Therefore, .
But and
.
Substitute these values into the volume equation and you get:
.

.
But some of the factors on the right side can be multiplied into a simpler form. The product
of is 36 and the product of is . Substituting
these into the volume equation results in:
.

.
For the given sphere whose surface area is the volume is:
.

.
Hope this helps you to understand the relationship between the surface area and volume
equations for a given sphere.
RELATED QUESTIONS
The surface area of a sphere is 64 pi m^2. Find the volume of the sphere in terms of pi. (answered by jim_thompson5910)

The surface area of a sphere is 3600 pi square inches. If v represents the volume of the... (answered by Theo)

A sphere is inscribed in a cube whose surface area is 36 square units. Determine the... (answered by scott8148)

Sphere B has 4 times the surface area of sphere A. How many times the volume of sphere A... (answered by richwmiller,amoresroy)

The surface area of a sphere 324 square centimeters. What is volume in cubic centimeters, (answered by Alan3354)

A metallic right circular cone of volume 36 pi is melt into a sphere.what is the surface... (answered by Fombitz)

Find the volume of a sphere, whose radius is 6 meters. Leave your answer in terms of... (answered by Alan3354)

Find the volume of a sphere whose radius is 1cm (expres your answer in terms of... (answered by mouk)

If the volume of a sphere is 3000 pi, what is the surface area? (answered by fractalier)