Question

For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is 4 3 π r 3 , where r is the radius.)

Answer 1

Answer:

The radius of the new cheese ball formed is approximately 6.603 inches.

Step-by-step explanation:

We are given the following in the question:

Radius of three cheese ball = 2 inches, 4 inches, and 6 inches

They were combined to form a new cheese ball.

Thus, we can write

Volume of three cheese balls =  Volume of new cheese ball.

Let r be the radius of new cheese ball.

Volume of sphere =

$\displaystyle\frac{4}{3}\pi r^3$

Putting values, we get:

$\displaystyle\frac{4}{3}\pi r_1^3 + \displaystyle\frac{4}{3}\pi r_2^3 +\displaystyle\frac{4}{3}\pi r_3^3 =\displaystyle\frac{4}{3}\pi r^3\\\\\frac{4}{3}\pi(2^3 + 4^3 + 6^3) = \displaystyle\frac{4}{3}\pi r^3\\\\2^3 + 4^3 + 6^3 = r^3\\\Rightarrow 288 = r^3\\\Rightarrow r = (288)^{\frac{1}{3}}\\\Rightarrow r \approx 6.603$

Thus, the radius of the new cheese ball formed is approximately 6.603 inches.