Module 5 · Mensuration
Chapter 49: 3D Mensuration
Mensuration
4 topics
What this chapter covers
The 4 topics below make up 3D Mensuration on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Volume of standard solids
| Cube (side a) | V = a³ |
|---|---|
| Cuboid (l, b, h) | V = l × b × h |
| Cylinder (radius r, height h) | V = πr²h |
| Cone (radius r, height h) | V = ⅓πr²h |
| Sphere (radius r) | V = (4/3)πr³ |
| Frustum (radii R, r; height h) | V = (1/3)πh(R² + Rr + r²) |
Surface area, slant & diagonal
| Cube TSA / diagonal | TSA = 6a², diagonal = a√3 |
|---|---|
| Cuboid TSA / diagonal | TSA = 2(lb + bh + hl), diag = √(l²+b²+h²) |
| Cylinder CSA / TSA | CSA = 2πrh, TSA = 2πr(r + h) |
| Cone slant & CSA / TSA | l = √(r²+h²), CSA = πrl, TSA = πr(r + l) |
| Sphere / Hemisphere area | Sphere = 4πr²; Hemisphere CSA = 2πr², TSA = 3πr² |
| Frustum slant & CSA | l = √(h² + (R−r)²), CSA = πl(R + r) |
CAT reference
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