Question

The radius of the cone id 1.75 inches an the height id 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches what is the closest approximation of the volume of the cone

Answer 1

Answer: $11.15 in^{3}$

Explanation:

We need to know the volume of the cone that can be filled with bubble gum ball, but firstly we need to calculate the volume of the cone $V_{C}$ and the volume of the buble gum ball (a sphere) $V_{B}$:

Volume of the cone:

$V_{C}=\frac{\pi R^{2}h}{3}$ (1)

Where:

$R=1.75 in$ is the radius of the cone

$h=3.5 in$ is the height of the cone

$V_{C}=\frac{\pi (1.75 in)^{2}3.5 in}{3}$ (2)

$V_{C}=11.22 in^{3}$ (3) This is the volume of the cone

Volume of the gum ball:

$V_{B}=\frac{4\pi r^{3}}{3}$ (4)

Where:

$r=\frac{0.5 in}{2}=0.25 in$ is the radius of the sphere (half the diameter)

$V_{B}=\frac{4\pi (0.25 in)^{3}}{3}$ (5)

$V_{B}=0.065 in^{3}$ (6) This is the volume of the gum ball

Know we are able to find the closest approximation of the volume of the cone that can be filled with bubble gum ball, by calculating the difference or substracting (6) from (3):

$V_{C}-V_{B}=11.22 in^{3}-0.065 in^{3}$ (7)

Finally:

$V_{C}-V_{B}=11.15 in^{3}$ (8)