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Lesson

Composite Solids and Recasting

A frustum is formed when the top of a cone is cut parallel to the base, removing a smaller cone. Its curved surface area is π(r₁ + r₂)l and its volume is (1/3)πh(r₁² + r₂² + r₁r₂). Frustums appear in buckets, lampshades, frustum-shaped pots, and industrial moulds.

45min lesson

Objectives3 goals Lesson10 blocks Review11 assets Practice32 items

Learning objectives

What to understand

3 goals

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Understand composite solids and recasting in the Mensuration chapter.
Connect the idea with formulas, examples, and exam-style questions.
Use flashcards, notes, MCQs, and LAQs to check readiness.

Lesson

Step-by-step lesson

10 sections

Example

Finding the Curved Surface Area of a Cone

Find the curved surface area of a cone with radius 5 cm and slant height 13 cm. 1. Use CSA = πrl. 2. Substitute r = 5.0, l = 13.0. 3. CSA = 65.0*π square units. Final answer: 65.0*π Exam tip: Ensure you use the slant height in your calculations for curved surface area. Common mistake: Using the perpendicular height instead of the slant height.

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10 lesson sections8 cards / 3 notes18 MCQs / 14 written questions

Lesson Notes Flashcards Revision MCQs Written answers Topic test

Notes

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3 notes

Review the compact notes before moving into recall.

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1
Frustum of a Cone: Truncated Solids
2
Combining Solids and Composite Figures
3
Melting and Recasting: Conservation of Volume

Practice

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32 prompts

18 MCQs14 LAQsMixed test

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In this chapter

Mensuration

Topic 6 of 7

Now on Composite Solids and Recasting. Next up: Scaling and Applications.

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Frustum of a Cone
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Composite Solids and Recasting

What to understand

Step-by-step lesson

Finding the Curved Surface Area of a Cone

Finding the Volume of a Cylinder

Frustum of a Cone: Truncated Solids

Combining Solids and Composite Figures

Melting and Recasting: Conservation of Volume

The curved surface area of a cylinder

The total surface area of a cylinder

The volume of a cylinder

The curved surface area of a cone

The total surface area of a cone

Finding the Curved Surface Area of a Cone

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Note highlights

Frustum of a Cone: Truncated Solids

Combining Solids and Composite Figures

Melting and Recasting: Conservation of Volume

Check this topic

Mensuration

Mark this topic complete

Around this topic

Composite Solids and Recasting

What to understand

Step-by-step lesson

Finding the Curved Surface Area of a Cone

Finding the Volume of a Cylinder

Frustum of a Cone: Truncated Solids

Combining Solids and Composite Figures

Melting and Recasting: Conservation of Volume

The curved surface area of a cylinder

The total surface area of a cylinder

The volume of a cylinder

The curved surface area of a cone

The total surface area of a cone

Finding the Curved Surface Area of a Cone

Choose your next activity

Note highlights

Frustum of a Cone: Truncated Solids

Combining Solids and Composite Figures

Melting and Recasting: Conservation of Volume

Check this topic

Mensuration

Mark this topic complete

Around this topic