Class 9 Maths • Chapter 11 • Comprehensive Guide
A cone is a 3D shape generated by rotating a right-angled triangle around one of its perpendicular sides. Think of an ice-cream cone or a birthday hat!
Net of a Cone
A cylinder has two circular bases and one curved surface. Example: water tank, drum, pipe.
Input Radius (r) and Height (h) to find everything!
A sphere is the set of all points in 3D space equidistant from a center point.
Sphere Area = \(4\pi r^2\)
| Shape | CSA / LSA | Total Surface Area | Volume |
|---|---|---|---|
| Cone | \( \pi r l \) | \( \pi r (l + r) \) | \( \frac{1}{3} \pi r^2 h \) |
| Sphere | \( 4 \pi r^2 \) | \( 4 \pi r^2 \) | \( \frac{4}{3} \pi r^3 \) |
| Hemisphere | \( 2 \pi r^2 \) | \( 3 \pi r^2 \) | \( \frac{2}{3} \pi r^3 \) |
| Solid | TSA | Volume |
|---|---|---|
| Cuboid | \(2(lb + bh + hl)\) | \(l \times b \times h\) |
| Cube | \(6a^2\) | \(a^3\) |
Volume represents the space occupied, while Capacity is the amount of liquid a container can hold.
Convert Volume (cm³) to Liters
| Property | Sphere | Hemisphere |
|---|---|---|
| CSA | \(4\pi r^2\) | \(2\pi r^2\) |
| TSA | \(4\pi r^2\) | \(3\pi r^2\) |
| Volume | \( \frac{4}{3}\pi r^3 \) | \( \frac{2}{3}\pi r^3 \) |
A water tank is in the shape of a cylinder surmounted by a hemisphere. Radius = 7 m, height of cylindrical part = 10 m.
Assertion (A): Volume of a cone is one-third the volume of a cylinder.
Reason (R): Both have same base radius and height.
✔ Both A and R are true and R explains A
1. The slant height 'l' of a cone is given by:
2. The Total Surface Area of a Hemisphere is:
3. If radius of a sphere is doubled, surface area becomes:
4. Volume of a cone is ______ the volume of a cylinder with same r and h.
5. How many liters in 1 m³?