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How to find the surface area and volume of cones

Grade 10 Math: Master Essential Skills & Concepts

1.1 Solving Problems Involving Similar Triangles

Similar triangles

Similar polygons

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

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Combining the exponent rules

Isosceles and equilateral triangles

2.1 Solving Problems Involving the Trigonometry of Right Triangles

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

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 = o / a)

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

3.1 Solving Problems Involving Surface Area and Volume, Using the Imperial and Metric Systems of Measurement

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

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

1.1 Manipulating and Solving Algebraic Equations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Introduction to linear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

2.1 Graphing and Writing Equations of Lines

Slope 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>

Point-slope 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 slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

3.1 Solving and Interpreting Systems of Linear Equations

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 systems of linear equations by graphing

Applications of linear equations

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

1.1 Manipulating Quadratic Expressions

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

2.1 Identifying Characteristics of Quadratic Relations

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

3.1 Solving Problems by Interpreting Graphs of Quadratic Relations

Applications of quadratic functions

Applications of quadratic equations

Parent Assignments

Challenge Zone

Foundation Review

<p>Get better math marks with our complete Grade 10 math help &ndash; be it <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grades.html">Ontario math curriculum</a>, math curricula of <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=foundations10">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces. We&apos;ve got you all covered!</p>

<p>Just like your class or textbook, our complete help for grade 10 math includes topics such as Trigonometry, Quadratic Equations, Radicals, Factoring polynomials, Linear equations, Linear systems, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 10 math problems. Then, strengthen your understanding with tons of grade 10 math practice.</p> 

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Foundations of Mathematics, Grade 10, Applied (MFM2P) 

1. Measurement and Trigonometry

2. Modelling Linear Relations

3. Quadratic Relations of the Form y = ax^2 + bx + c

math

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<p>Getting ahead of the game is always recommended for aspiring students and math keeners! Partnering with StudyPug as your tutor is the best way to do so as we offer a plethora of math courses to prepare you well in advance for the future! Whether you feel like the grade 9 math curriculum is too easy, or find yourself in search of a challenge, or perhaps have had enough of grade 9 math worksheets, StudyPug is here to save you from boredom and grow your potential. Master grade 10 math ahead of time or swing back to refresh your memory on <a href="[[region_textbook.html|{"textbook_key":"grade9"}]]">grade 9 math</a> anytime and everywhere. Many topics learnt in grade 9 math will be expanded on in grade 10 math, so take your time, and have no shame in skipping back.</p>
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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.png

Ex. 1:

Finding surface area and volume of a cone with unit conversion

Finding surface area and volume of a cone-hemisphere composite solid

We just learned how to calculate the surface area and volume of pyramids and cylinders in the previous lessons. Now, we will look at cones - objects that have circle bases like cylinders and pointy tops like pyramids. Just like pyramids and cylinders, there are formulas for surface area and volume of cones. We will also try out some questions on composite solids that consist of cones too.

Circles and circumference 

Arcs of a circle

Surface area and volume of cones

What You'll Learn

Calculate the surface area of cones using the formula πr² + πrs

Apply the Pythagorean theorem to find the slant height of a cone

Compute cone volume using the formula (base area × height)

Convert between measurement units to ensure dimensional consistency

Solve for surface area and volume of composite solids combining cones with other shapes

What You'll Practice

Finding slant height using the Pythagorean theorem with radius and height

Calculating surface area and volume of cones with given dimensions

Converting between feet and inches before applying formulas

Working with composite solids like hemispheres combined with cones

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

2 Video lessons

Learning resources

Skills

Surface Area

Volume

Cones

Pythagorean Theorem

Slant Height

Composite Solids

Unit Conversion

3D Geometry