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Finding the surface area and volume of spheres

General Maths: Master Core Concepts & Problem Solving

Pythagorean Theorem

Squares and square roots

Square Root of a Perfect Square

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circles

Angles in a circle

Chord properties 

Tangent properties

Circle and circumference 

Circle properties

Arcs of a circle

Areas and sectors of circles

Inscribed Angles and Proofs

Central and inscribed angles in circles

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

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Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles 

Solving expressions using 30-60-90 special right triangles 

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

Sine Rule and Cosine Rule

Sine rule

Law of sines

Ambiguous case: SSA triangles

Cosine rule

Sine rule and cosine rule word problems

Applications of the sine law and cosine law

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Gradient intercept form: y = mx + b

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Perpendicular line equation

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Simultaneous Equations

Solving 3 variable simultaneous equations by substitution

Solving 3 variable systems of equations by substitution

Solving 3 variable simultaneous equations by elimination

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable simultaneous equations

Word problems relating 3 variable systems of equations

Solving 3 variable simultaneous equations with no or infinite solutions

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving simultaneous linear equations by graphing

Solving systems of linear equations by graphing

Solving simultaneous linear equations by elimination

Solving systems of linear equations by elimination

Solving simultaneous linear equations by substitution

Solving systems of linear equations by substitution

Simultaneous linear-quadratic equations

System of linear-quadratic equations

Simultaneous quadratic-quadratic equations

Operations with Algebraic Expressions

Partial fraction decomposition

Solving equations with algebraic fractions

Solving rational equations

Simplifying algebraic fractions and restrictions

Simplifying rational expressions and restrictions

Adding and subtracting algebraic fractions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying algebraic fractions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing algebraic fractions

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Applications of equations with algebraic fractions

Applications of rational equations

Simplifying complex fractions

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Application of Means

Range and outliers

Range and Outlier Word Problems

Outlier Word Problems

Range Word Problems

Find the Range

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Frequency distribution and histograms

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Bivariate Data

Scatter plots and correlation

Regression analysis

Equation of the best fit line

Sequences

Arithmetic sequences

Geometric sequences

Introduction to Matrices

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Properties of Matrices

Zero matrix

Identity matrix

Properties of matrix addition

Properties of scalar multiplication

Properties of matrix multiplication

Bearings

Introduction to bearings

Bearings and direction word problems

We&apos;ve got you covered with our complete help for General Maths, whether it&apos;s for <a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/mathematics-general.html">HSC</a> General Maths Exam (NSW), preparation for study of <a href="http://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/general/genmathindex.aspx">VCE Maths</a> at Unit 3 and 4 (Victoria), stage 2 General Maths assessment for <a href="https://www.sace.sa.edu.au/students/sace-overview/stage-2-assessment">SACE</a> (South Australia), or senior secondary Australian Curriculum for <a href="http://www.australiancurriculum.edu.au/seniorsecondary/mathematics/general-mathematics/curriculum/seniorsecondary#page=1">General Mathematics</a>.

Aligned with your maths syllabus or class, our General maths tutors cover help on topics like Linear functions, Simultaneous equations, Trigonometry, Algebraic expressions, Statistics, Matrix and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest general maths problems. Then, strengthen your understanding with tons of general maths practice.

All our lessons are taught by experienced General maths teachers. Let&apos;s finish your homework in no time, and ACE that exam.

General Maths

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Surface area and volume of spheres

What You'll Learn

Calculate the surface area of a sphere using the formula 4πr²

Calculate the volume of a sphere using the formula (4/3)πr³

Find surface area and volume of hemispheres by adjusting sphere formulas

Solve for radius using circumference when the circumference is given

Calculate surface area and volume of composite solids combining spheres and cylinders

What You'll Practice

Finding surface area and volume of hemispheres with exposed circular bases

Calculating dimensions of capsule-shaped solids (cylinder with spherical ends)

Converting between circumference and radius to solve problems

Adding surface areas and volumes of combined geometric shapes

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

2 Video lessons

Learning resources

Skills

Spheres

Surface Area

Volume

Composite Solids

Hemispheres

Cylinders

Circumference

3D Geometry