Volume of a Right Prism

• The lesson is on deriving and applying the formula for the volume of a right prism.
• The learning objective is to be able to calculate the volume of a right prism using the volume formula.

Well-being

• A question to consider is how technology plays a role in your life.
• You can manage screen time by going to wellbeing.google/reflect/.
• This is estimated to take approximately 4 minutes.

Standard/Learning Objectives

• The standard covers solving real-world mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Vocabulary

• Volume: The measure of the space a three-dimensional figure occupies.
• Rectangular Prism: Two parallel congruent bases that are rectangles.
• Triangular Prism: Two parallel congruent bases that are triangles.

Success Criteria

• You can explain how to derive and apply the formula for the volume of the prism
• You can accurately apply the formula to find the volume of right prisms.
• You can use the formula to find the volume of a rectangular prism.
• You can find the volume of a rectangular prism if the unit cubes inside it can be seen.

Starter Activity

• Calculate the area of squares, rectangles and triangles.
  • For a square, given a 2.5 in side, Area = .
  • For a rectangle, given 26 ft and 3 ft sides, Area = .
  • For a triangle, given 11 cm and 14 cm sides, Area = .
• Visit https://wordwall.net/resource/44821/maths/area-quiz.

Volume of Prisms

• Volume of Prism = Area of Base x Height
• The volume V of a prism is the product of the area with the base B and the height h.
  • Formula: V = Bh
  • For rectangular prisms V = length x width x height

Volume of Rectangular Prisms

• A jewelry box is in the approximate shape of a rectangular prism.
• The approximate volume of the jewelry box should be rounded to the nearest tenth if necessary.
  • The dimensions of the box are 18.4 cm x 14.8 cm x 25.6 cm.
    • V = Bh
    • V = (lw)h
    • V = (18.4 • 14.8)25.6
    • V = 6,971.392
  • The volume of the jewelry box is about 6,971.4 cubic centimeters.

Real Life Application

• Find the volume of a rectangular prism.
  • A rectangular sandbox measures 4 feet by 7 feet by 2 feet can hold.
• Find the volume of the triangular prism.
• volume of triangular prism = area of cross-section × length
  • A triangular prism has a base length of 1.5 centimeters, a base height of 3 centimeters, and a height of 12 centimeters. Find the volume of

Tasks

• Differentiated Task A: Find the volume of each of the figures.
  • Cuboid 8 cm x 4 cm x 5 cm
  • Prism b = 4.5, h = 5, l = 8 Visit https://http://www.mathgames.com/skill/5.120-volume-of-cubes-and-rectangular-prisms
• Differentiated Task B:
  • Triangular prism b = 3.1m, h = 2.5m, l = 6m
  • A triangular prism is shown. If the length x if its volume is 72 cubic feet and the dimensions are given as 12 ft and 3 ft. Visit https://www.ixl.com/math/grade-6/volume-of-cubes-and-rectangular-prisms
• Differentiated Task C: Find the missing dimension of the rectangular prism
  • Volume = 72 in. to the third power
  • Volume = 1380 cm to the third power

Challenge

• Find the Error A classmate found the height of the prism shown using the following method. Find the error and correct it.
  • h = 1.5(1.2)(2.5) = 4.5 cm

Evaluate Links

• https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/imp-finding-volume/e/volume_1
• https://quizizz.com/admin/quiz/5ca8l1e1c6a145001a10b38a/volume-of-rectangular-prisms?source=MainHeader&page=FeaturedPage
• https://dashboard.blooket.com/set/65d3a4dd2f759ea15b76aebf

Self Assessment

• Assess how well you can calculate the volume of a right prism using the volume formula.