Surface areas & volumes
Cones, spheres, hemispheres and cylinders.
Learn with Kutty
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Surface area is the outside skin. Volume is the space inside.
Look: A cone: radius r, height h, slant l. Volume = ⅓πr²h.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Ball (sphere) of radius 3 cm: volume (leave π)?
2Cone r = 6, h = 8: slant?
3Cylinder r = 7, h = 10: volume (π = 22/7)?
! Careful!
✗Using the height h instead of slant l for the cone’s side.
✓The side uses l = √(r² + h²).
✗Forgetting the ⅓ for a cone.
✓A cone is ⅓ of a cylinder.
See the whole lesson on one page
Surface area is the outside skin. Volume is the space inside.
Each solid has its own rules. A cone holds one third of the cylinder with the same base and height. A ball (sphere) has volume ⁴⁄₃πr³.
Think of it like thisWrapping paper for a gift box is its surface area. The sweets you fit inside fill its volume.
- Slant (l)
- From the tip down the side to the edge.
Solved together
An ice-cream cone has radius 3.5 cm and height 12 cm. How much ice-cream fills it? (π = 22/7)
Cone volume = ⅓ × π × r × r × h.
⅓ × 22/7 × 3.5 × 3.5 × 1222/7 × 3.5 × 3.5 = 38.5. Then × 12 ÷ 3 = × 4.
38.5 × 4 = 154
Answer154 cm³ of ice-cream.
For older learners and grown-ups: a little more
Curved surface of a cone = πrl; of a cylinder = 2πrh; of a sphere = 4πr². Hemisphere volume = ⅔πr³.
Now practise it
Kanakku makes new questions on surface areas & volumes every time. It shows the working and gives a hint when you are stuck.