Question

Gary used candle molds, as shown below, to make candles that were perfect cylinders and spheres:

A cylindrical mold is shown, the radius of the top circular section of the cylinder is labeled 2 inches and the height of the cylinder is labeled as 4 inches. On the right side of this mold is a spherical mold. The radius of this spherical mold is labeled as 2 inches.

What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14.

16.75 cubic inches
20.93 cubic inches
24.25 cubic inches
33.49 cubic inches

Answer 1

The answer is the first option, which is: $16.75$ cubic inches.

The explanation for this answer is shown below.

1. You must apply the formula for calculate the volume of a cylinder and the formula for calculate the volume of a sphere and substitute the values which are given in the problem above, as following:

$Vc=\pi r^{2} h$

Where $h$ is the heigth of the cylinder and $r$ is the radius.

$Vc=(3.14)(2in)^{2} (4in)=50.24in^{3}$

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

Where $r$ is the radius of the sphere.

$Vs=\frac{4(3.14)(2in)^{3}}{3} =33.49in^{3}$

2. Then, you must susbtract both volumes to calculate the difference asked in the problem:

$V=50.24in^{3} -33.49in^{3} =16.75in^{3}$

3. Therefore, the answer is the option mentioned above.

Answer 2

Short and simple, 16.74 cubic inches