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Formulas and examples for calculating the circumference and volume of spheres using given measurements. It also includes a problem-solving section for determining the number of Skittles that can fit in a spherical jar and a challenge for calculating the volume of a cylindrical cup filled with gummy bears.
What you will learn
Typology: Lecture notes
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3D Measurements and Analysis
Review
Wrap a string around the widestpart of the sphere to measure the circumference. Lay the string against the ruler todetermine the measurement for circumference.
Determining Volume of Spheres
If circumference (C)= 15 cm
What is the diameter(D)? What is the radius? (r)
If circumference = 15 cm What is the diameter? 15 cm = π D (15 cm) / π = (π D) / πD = 15 cm / π D = 4.775 cm
If circumference = 15 cm What is the radius? 15 cm = 2(15 cm) / 2 π = (2 π r) / 2 π π r r = (15cm) / (2 π)r = 15 cm / (6.28) r = 2.389 cm
If radius == 2.389 cm (15 cm) / 2 π = 15 cm / (6.28)
Volume = (4/3) * 3.14 * (2.389 cm) 3 == 57.11 cm (4/3) * 3.14 * (13.635 cm) 3
If circumference of jar = 17 in What is the radius?17 in = 2 π r (17 in) / 2 π = (2 π r) / 2 πr = (17 in) / (2 π) r = ( 17 in) / (6.28318)r = 2.706 in
= (4/3) * 3.14 * (= (4/3) * 3.14 * (19.815 inin in)2.706 in) 3 = (4/3) * 3.14 * (19.815 in= 83.001 in 3 3 )
If you have a sphere jar of marbles. The jar has adiameter of 20 cm and a marble has a diameter of 1 cm. How many marbles can fit in the jar? Diameter = 20 cmradius = 10 cm
Volume = (4/3) * 3.14 * (10)^ Volume = 1.33 * 3.14 * 1000
Volume of Jar / Volume of Skittles 1,269 skittles in a completely spherical jar83.001 in^3 / 0.0654 in^3 Our jar was flat on the bottom so you may want to remove a few skittles.
Volume of a Cylinder Challenge: Volume = π * 2 * r * h How many gummy bears would fit into acylindrical cup? Measure the gummy bears by (lwh) Measure your cup’s height and diameter.Measure the gummy bear.