Question

Jade used candle molds, as shown, 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 3 inches and the height of the cylinder is labeled as 7 inches. On the right side of this mold is a spherical mold. The radius of this spherical mold is labeled as 3 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.)

Answer 1

The approximate difference in the amount of wax needed to make a candle from each of these molds is 84.78 cubic inches.

Step-by-step explanation:

To find the difference in the amount of wax needed to make a candle from each of these molds, we need to calculate the volume of each shape.

For the cylindrical mold, the volume can be calculated using the formula V = πr²h, where r is the radius and h is the height. Plugging in the values, we get V = 3.14 × (3 inches)² × 7 inches = 197.82 cubic inches.

For the spherical mold, the volume can be calculated using the formula V = (4/3)πr³. Plugging in the values, we get V = (4/3) × 3.14 × (3 inches)³ = 113.04 cubic inches.

Therefore, the approximate difference in the amount of wax needed to make a candle from each of these molds is 197.82 cubic inches - 113.04 cubic inches = 84.78 cubic inches.

Answer 2

`Difference = 85\ in^3`

Step-by-step explanation:

Given

Cylinder:

`Height = 7\ inches`

`Radius = 3\ inches`

Sphere

`Radius = 3\ inches`

Required

Determine the difference in amount of wax needed in both

To do this, we first calculate the volume of both

`Volume_(cylinder) = \pi r^2h`

`Volume_(cylinder) = 3.14 * 3^2 * 7`

`Volume_(cylinder) = 3.14 * 9 * 7`

`Volume_(cylinder) = 197.82\ in^3`

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

`Volume_(sphere) = (4)/(3) *3.14 * 3^3`

`Volume_(sphere) = (4)/(3) *3.14 * 27`

`Volume_(sphere) = 113.04\ in^3`

Then calculate the difference:

`Difference = Volume_(cylinder) - Volume_(sphere)`

`Difference = 197.82in^3 - 113.04in^3`

`Difference = 84,78in^3`

`Difference = 85\ in^3` -- Approximated