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Surface Area of a Cylinder

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Surface Area of a Cylinder

Study Guide

Key Definition

The surface area of a cylinder is calculated using the formula $T.S.A. = 2 \pi r h + 2 \pi r^2$, where $r$ is the radius and $h$ is the height.

Important Notes

The lateral surface area is $2 \pi r h$
The base area of a cylinder is $\pi r^2$
Surface area is measured in square units
Always use the same units for all measurements
The formula $T.S.A.$ includes both the lateral and base areas

Mathematical Notation

$\pi$ represents the constant approximately equal to 3.14159

$r$ is the radius of the base

$h$ is the height of the cylinder

$2 \pi r h$ is the lateral surface area

$\pi r^2$ is the area of the base

Remember to use proper notation when solving problems

Why It Works

The formulas leverage the properties of circles and the height of the cylinder to calculate the surface area, accounting for both the side and the two circular bases.

Remember

For a cylinder, always consider both the lateral and the base areas for the total surface area.

Quick Reference

Lateral Surface Area:$2 \pi r h$

Total Surface Area:$2 \pi r h + 2 \pi r^2$

Understanding Surface Area of a Cylinder

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The lateral surface area is like unrolling the side of the cylinder into a rectangle with one side $2 \pi r$ and the other $h$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the lateral surface area of a cylinder with a radius of $3$ inches and height of $9$ inches?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you need to paint a cylindrical water tank with radius $5$ meters and height $7$ meters. Calculate the total surface area to determine how much paint is needed.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A cylinder has a height that is twice its radius. If the radius is $4$ cm, what is the total surface area?

Challenge Quiz

Single Choice Quiz

Advanced

A cylindrical container has a total surface area of $300 \pi \text{ cm}^2$. If its radius is $5$ cm, what is its height?

Recap

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Review key concepts and takeaways