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Calculating the Volume of Spheres and Other Shapes: A Review, Lecture notes of Pre-Calculus

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

  • What is the formula for calculating the circumference of a sphere?
  • What is the formula for calculating the volume of a sphere?
  • How do you find the radius of a sphere given its circumference?
  • What is the volume of a cylindrical cup filled with gummy bears if its height and diameter are given?
  • How many Skittles can fit in a spherical jar with a circumference of 15 cm?

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

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Calculating Volume
3D Measurements and Analysis
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Download Calculating the Volume of Spheres and Other Shapes: A Review and more Lecture notes Pre-Calculus in PDF only on Docsity!

Calculating Volume

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

C = 2 * π * r or C = π * D

If circumference (C)= 15 cm

What is the diameter(D)? What is the radius? (r)

C = π * D

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

C = 2 * π * r

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

V = (4/3) π * r 3

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

C = 2 * π * r

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

Volume of Jar

= (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

Calculating the Number of Skittles

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.