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 43πr343πr3, where r is the radius.)

Answer 1

Here we need to find the volume of each spherical ball using the given values of the diameter and then we combine those values and find the diameter .

For the first ball, diameter is 2 inches, so radius =1 inches

For the second ball, diameter is 4 inches, so radius = 2 inches

For the third ball, diameter is 6 inches, so radius =3 inches.

Now we use the given formula of the volume of sphere.

$V_{1} = \frac{4}{3} \pi (1)^3, V_{2} = \frac{4}{3} \pi (2)^3,V_{3} = \frac{4}{3} \pi (3)^3$

$V_{1} = 4.2 , V_{2} =16.755, V_{3}= 37.7$

Total volume = 4.2 +16.755 + 37.7 =58.655

Now we have the volume and using the given formula of volume of spher, we can find out the radius .

$58.655= \frac{4}{3} \pi r^3$

$r = 2.4$

So diameter = 2 * 2.4 = 4.8 inches