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

Answer:

$Difference = 85\ in^3$

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

$Volume_{cylinder} = \pi r^2h$

$Volume_{cylinder} = 3.14 * 3^2 * 7$

$Volume_{cylinder} = 3.14 * 9 * 7$

$Volume_{cylinder} = 197.82\ in^3$

$Volume_{sphere} = \frac{4}{3}\pi r^3$

$Volume_{sphere} = \frac{4}{3} *3.14 * 3^3$

$Volume_{sphere} = \frac{4}{3} *3.14 * 27$

$Volume_{sphere} = 113.04\ in^3$

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