Q1. What is the shape formed by cutting the top of a cone?
✔ When the top part of a cone is removed parallel to the base, the remaining solid is called a frustum.
Q2. If R=5, r=2, h=4, what is the slant height l?
✔ Using Pythagoras theorem: l = sqrt(4^2 + (5-2)^2) = sqrt(16+9) = sqrt(25) = 5.
Q3. Which formula calculates the Curved Surface Area of a frustum?
✔ The correct formula for Curved Surface Area is pi times slant height times the sum of radii.
Show transcript
[Slide 1] What is a Frustum?
Imagine slicing the top off an ice cream cone. The bottom part left behind is called a frustum. It has two circular bases of different radii.
[Slide 2] Key Formulas to Remember
We need specific formulas for curved surface area and volume. Remember slant height is key here. Let's look at the curved surface area formula first.
[Slide 3] Worked Example Setup
Let's solve a problem. Large radius is 5, small is 2, height is 4. First, calculate the slant height using Pythagoras theorem.
[Slide 4] Worked Example Calculation
Slant height equals 5. Now substitute into the area formula. The curved surface area comes out to be 35 pi square units.
[Slide 5] Common Student Mistake
A common mistake is using vertical height instead of slant height. Always calculate slant height separately before finding area.
[Slide 6] Quick Recap
To recap, identify the frustum and its dimensions. Find slant height first, then apply the volume or area formulas carefully.