Surface Area and Volume — Class 9 Maharashtra SSC Mathematics revision notes
A 3-page visual revision sheet for Surface Area and Volume, written for Class 9 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Surface Area and Volume in one look
the flat faced solids and the round ones, and reading which of the two a question wants
Two quantities, two sets of units
- volume is the space a solid fills, measured in cubic units such as cm³
- surface area is the skin of the solid, measured in square units such as cm²
- lateral or curved surface area leaves out the top and bottom faces and counts only the sides
- total surface area counts every face the solid actually has
- the wording decides which: painting, covering or wrapping wants area, while filling, holding or capacity wants volume
- a solid open at the top, such as a tank or a box without a lid, does not count that face
The flat faced solids
- cuboid, volume
V = lbh - cuboid, total surface then lateral
2(lb + bh + hl),quad 2h(l + b) - cube of edge a, volume then surface
a^3,quad 6a^2 - diagonal of a cuboid
d = √l^2 + b^2 + h^2 - diagonal of a cube
d = a√3
The round solids
- cylinder, curved then total surface
2π rh,quad 2π r(h + r) - cylinder, volume
V = π r^2 h - cone, curved then total surface
π rl,quad π r(l + r) - cone, volume
V = 1/3π r^2 h - sphere, surface then volume
4π r^2,quad 4/3π r^3 - the cone's three lengths
l^2 = r^2 + h^2
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Surface Area and Volume sheet covers
- Surface area
- Volume
- Lateral surface area
- Two quantities, two sets of units
- The flat faced solids
- cuboid, volume
- cuboid, total surface then lateral
- cube of edge a, volume then surface
- diagonal of a cuboid
- diagonal of a cube
- The round solids
- cylinder, curved then total surface
- cylinder, volume
- cone, curved then total surface
- cone, volume
- sphere, surface then volume
- the cone's three lengths
- A cylinder, both quantities
- Reading the wording
- Working backwards to a dimension
- Which quantity the words point to
- Symbols in this chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Surface Area and Volume the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.