Homepage

Course Index

Build a Quiz

Subscriptions

Courses

NSW Y8 Maths

Topics

Pythagoras Working with Numbers Algebra Equations Geometry Area and Perimeter Volume Fractions and Percentages Investigating Data Congruent Figures Probability Rates and Ratios Graphing Linear Equations Time and Travel

NSW Y8 Maths Volume Composite Shapes for Volume

Resources for Composite Shapes for Volume

  • Questions

    10

    With Worked Solution
    Click Here
  • Video Tutorials

    2


    Click Here

Composite Shapes for Volume Theory

\begin{multicols}{2} \textbf{Example 1}\\ Find the volume of the composite solid.\\ \begin{center} \begin{tikzpicture}[scale=0.55,line width=1pt] \coordinate[label=above:] (O) at (0,0); \coordinate[label=right:] (B) at (90:3); \coordinate[label=left:] (A) at (right:5); \begin{scope}[shift=(B)] \coordinate[label=left:] (C) at (right:5); \end{scope} \begin{scope}[shift=(B)] \coordinate[label=left:] (D) at (60:2); \end{scope} \begin{scope}[shift=(D)] \coordinate[label=left:] (F) at (right:3); \end{scope} \begin{scope}[shift=(C)] \coordinate[label=left:] (E) at (60:4); \end{scope} \begin{scope}[shift=(F)] \coordinate[label=left:] (G) at (60:2); \end{scope} \begin{scope}[shift=(G)] \coordinate[label=left:] (H) at (right:2); \end{scope} \begin{scope}[shift=(H)] \coordinate[label=left:] (I) at (-90:3); \end{scope} \draw (O)--(B) node[left,midway]{3 cm}--(C)--(A)--node[below,midway]{5 cm} cycle; \draw (B)--(D) node[left,midway]{2 cm} --(F)node[above,midway]{3 cm}--(G)--(H) edge (C); \draw (H)--(I)--(A) node[right,midway]{4 cm}; \end{tikzpicture} \end{center} \textbf{Example 1 solution}\\ \(\begin{aligned} \text { Area of top } & =3 \times 2+4 \times 2 \\ & =6+8 \\ & =14 \text{~cm}^2 \end{aligned}\)\\ \(\begin{aligned} \therefore \text { Volume of solid } & =14 \times 3 \\ & =42 \text{~cm}^3 \end{aligned}\) \columnbreak \textbf{Example 2}\\ Find the volume of the composite solid.\\ \begin{center} \begin{tikzpicture}[scale=0.45] \def\l{6} \def\w{6} \def\h{8} \coordinate (A) at (0,0,0); \coordinate (B) at (\l,0,0) ; \coordinate (C) at (\l,\w,0); \coordinate (D) at (0,\w,0); \coordinate (E) at (0,0,\h); \coordinate (F) at (\l,0,\h); \coordinate (G) at (\l,\w,\h); \coordinate (H) at (0,\w,\h); %Ecken \node[left= 1pt of A]{}; \node[right= 1pt of B]{}; \node[right= 1pt of C]{}; \node[left= 1pt of D]{}; \node[left= 1pt of E]{}; \node[right= 1pt of F]{}; \node[right= 1pt of G]{}; \node[left= 1pt of H]{}; %Kanten \draw[line width=1pt] (B) node[midway, below]{} -- (C) node[right,midway]{} -- (D) node[midway, above]{}; \draw[line width=1pt] (B) -- (F)node[midway,right,yshift=-2pt]{8 cm} -- (G) -- (C); \draw[line width=1pt] (G) -- (H) -- (D); \draw[line width=1pt] (E) -- (F) node[midway, below]{6 cm}; \draw[line width=1pt] (E) -- (H)node[left,midway]{6 cm}; \begin{scope}[shift=(230:3.2),yshift=0.5cm] \draw[line width=1pt] (0,0)--(4,0) node[below=-2pt,midway] {4 cm}--(2,4)--cycle; \draw[line width=1pt] (0,0) edge (30:2); \draw[|-|] (-0.4,0)--(-0.4,4) node[rectangle, fill=gray!10!white,pos=0.7,inner sep=1pt,right=-5pt] {\small 4 cm}; \end{scope} \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ For the triangular prism\\ \(\begin{aligned} \text { base area } & =\frac{1}{2} \times 4 \times 4 \\ & =8 \text{~cm}^2 \\ \therefore \text { Volume } & =8 \times 8 \\ & =64 \text{~cm}^3 \end{aligned}\)\\ For the rectangular prism.\\ \(\begin{aligned} \text { base area } & =6 \times 6 \\ & =36 \text{~cm}^2 \\ \therefore \text { Volume } & =36 \times 8 \\ & =288 \text{~cm}^3 \end{aligned}\)\\ \(\begin{aligned} \therefore \text { Volume of solid } & =288-64 \\ & =224 \text{~cm}^3 \end{aligned}\) \end{multicols}

Create account

Access content straight away with a two week free trial

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Composite Shapes for Volume.

  • Composite Shapes for Volume - Video - Composite Shapes for Volume 1

    You must be logged in to access this resource

  • Composite Shapes for Volume - Video - Composite Shapes for Volume 2

    You must be logged in to access this resource

Plans & Pricing

With all subscriptions, you will receive the below benefits and unlock all answers and fully worked solutions.

  • Teachers Tutors
    Features
    Free
    Pro
    All Content
    All courses, all topics
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Quizbuilder
     
    Class Results
     
    Student Results
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions
  • Awesome Students
    Features
    Free
    Pro
    Content
    Any course, any topic
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Basic Results
     
    Analytics
     
    Study Recommendations
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions