Math 10Chapter 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 (mm3), cm (cm3), m (m3), etc. Imperial: cubic in. (in3), ft. (ft3), yd. (yd3), etc.

Liquids and Gases Metric: millilitre (ml), litre (l), etc. Imperial: fluid ounce (oz), quart (qt),

gallon (gal)

Volume Formulas

Volume: 1/3(πr2)h

Volume Formulas Right Pyramid

Atriangle = 1/2bs Abase = b2

SA = 2bs + b2

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(πr3)

Volume 2/3(πr3)

Extra Practice

Pg. 42-44, # 4,6,8,9,10,11,18

Pg. 51-52, # 3-5,11,16

Do this in your homework books Show ALL your calculations!