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

Short and simple, 16.74 cubic inches

Answer 2

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=(4)/(3)r^(3) \pi`

Where
`r` is the radius of the sphere.

`Vs=(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.