Math 10 Chapter 1 - Geometry of 3-D Figures Lesson 5 – Calculating Volumes of 3-D Shapes

Todays Objectives: In this section we will: Sketch a diagram to represent a problem that involves volume(V) Determine the V of a right cone, right prism, right pyramid, or sphere using an object or diagram Determine an unknown dimension of a right cone, right prism, right pyramid, or sphere given the V and remaining dimensions Solve a problem that involves V

Volume Volume is the amount of 3-dimensional (3-D) space that a figure occupies or contains Consider again a box. The “amount” of air (or other substance) that fits inside the box is its volume. This is often referred to as the capacity of a container.

Units of Volume We use different units of volume depending on the state of what is being measured: Solids Metric: cubic mm (mm 3 ), cm (cm 3 ), m (m 3 ), etc. Imperial: cubic in. (in 3 ), ft. (ft 3 ), yd. (yd 3 ), etc. Liquids and Gases Metric: millilitre (ml), litre (l), etc. Imperial: fluid ounce (oz), quart (qt), gallon (gal)

Volume Formulas Volume: 1/3(πr 2 )h

Volume Formulas Right Pyramid A triangle = 1/2bs Abase = b 2 SA = 2bs + b 2 Volume = 1/3(base area)h

Volume Formulas Right Prism SA = 2(hl + lw + hw) Volume = lwh Volume = (base area)h

Volume Formulas Volume = (Base Area)h

Volume Formulas Volume 4/3(πr 3 ) Volume 2/3(πr 3 )

Extra Practice Pg , # 4,6,8,9,10,11,18 Pg , # 3-5,11,16 Do this in your homework books Show ALL your calculations!