CBSE · Class 6-12

Class 9 · Ganita Manjari

Unit 14 · Class 9Ganita Manjari

Math of Space: Surface Area and Volume

Surface areas and volumes of the standard solids — cuboid, cube, cylinder, cone, sphere, hemisphere.

Lessons

3 concepts

1
Curved vs Total Surface Area
CSA is the curved lateral surface only. TSA adds the flat circular ends (for cylinder, cone, hemisphere). Cuboids/cubes have no curved surface, so LSA and TSA both make sense in the flat-face sense.
2
Why the $\tfrac{1}{3}$ in the Cone Volume
Fill a cylindrical vessel of the same radius and height with sand three times, and it exactly fills a cone of the same base and height. Volume of cone is one-third that of a cylinder — a result Archimedes proved 2200 yea…
3
Slant Height of a Cone
The slant $\ell$ is the straight-line distance from the tip to a point on the base circumference. Pythagoras on the triangle formed by radius, height and slant: $\ell^2 = r^2 + h^2$ .

Skills to practise

Skill · medium

Math of Space: Surface Area and Volume — Practice