Kristy most likely used the formula for the volume of a cone, not the volume of a sphere.
Practice makes perfect
Kristy said that the volume of the sphere below is 144π cubic units. We know that her answer is incorrect. We want to find the mistake that Kristy made.
We will begin by finding the correct volume. Recall that the volume of a sphere is four thirds the product of π and the cube of the radius.
V=4/3π r^3From the diagram we can see that the radius is 6. This means we can substitute 6 for r in the formula. Then we will simplify the right-hand side.
The volume of the sphere is 288 cubic units. Let's compare this to the result that Kristy got.
V = 288 π ✓
V = 144π *
We see that the volume of the sphere is exactly twice the volume that Kristy came up with. This suggests that Kristy may have used a wrong formula.
288π=2( 144π)
Let's now recall an important relationship between volumes of cones and spheres.
A volume of a sphere is the same as twice the volume of a cone with the same circular base and height.
Kristy most likely used the formula for the volume of a cone, not the volume of a sphere. This could be why her answer is exactly half the actual volume of the sphere.
