Class 9 Maths — Chapter 11: SURFACE AREAS AND VOLUMES

What you'll learn

• ▸Introduction to Right Circular Cones
• ▸Relationship between Height, Radius, and Slant Height
• ▸Curved Surface Area (CSA) of a Cone
• ▸Total Surface Area (TSA) of a Cone
• ▸Applications of Cone Surface Area
• ▸Surface Area of a Sphere
• ▸Surface Area of a Hemisphere

Chapter Summary

--- PAGE 1 --- CHAPTER 11 SURFACE AREAS AND VOLUMES 11.1 Surface Area of a Right Circular Cone We have already studied the surface areas of cube, cuboid and cylinder. We will now study the surface area of cone. So far, we have been generating solids by stacking up congruent figures. Incidentally, such figures are called prisms. Now let us look at another kind of solid which is not a prism (These kinds of solids are called pyramids.). Let us see how we can generate them. Activity : Cut out a right-angled triangle ABC right angled at B. Paste a long thick string along one of the perpendicular sides say AB of the triangle [see Fig. 11.1(a)]. Hold the string with your hands on either sides of the triangle and rotate the triangle about the string a number of times. What happens? Do you recognize the shape that the triangle is forming as it rotates around the string [see Fig. 11.1(b)]? Does it remind you of the time you had eaten an ice-cream heaped into a container of that shape [see Fig…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Show real-world cone examples? Get Solution →
2. Explain cone formulas simply? Get Solution →
3. Compare cones to cylinders? Get Solution →
4. What is the formula for the Curved Surface Area of a right circular cone? Get Solution →
5. According to the text, what is the formula for the Surface Area of a Sphere with radius r? Get Solution →
6. What is the relationship between a cone's height (h), radius (r), and slant height (l)? Get Solution →
7. What is the formula for the Total Surface Area of a Hemisphere? Get Solution →
8. What solid shape is generated by rotating a right-angled triangle about one of its perpendicular sides? Get Solution →

Did you know?

• 💡 Ice cream cones became widely popular after their debut at the 1904 World's Fair.
• 💡 Many volcanoes are naturally occurring cones, formed by layers of cooling lava and ash.
• 💡 Spinning a flat triangle around an axis creates a 3D cone, a fundamental geometric solid.
• 💡 Unfolding a cone's curved surface reveals it's just a sector of a larger flat circle.
• 💡 Ancient Greek mathematicians like Archimedes pioneered methods for calculating cone volumes.

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