---
source: ncert
topic: mensuration
class_level: class_9
chapter: ch13
difficulty: intermediate
---

Class 9 | Ch13: Surface Areas and Volumes
SURFACE AREA AND VOLUME FORMULAS:
CUBOID: l=length, b=breadth, h=height.
Total SA=2(lb+bh+lh). Lateral SA=2(l+b)h. Volume=lbh. Diagonal=sqrt(l^2+b^2+h^2).
CUBE: side=a.
Total SA=6a^2. Lateral SA=4a^2. Volume=a^3. Diagonal=a*sqrt(3).
CYLINDER: r=radius, h=height.
Curved SA=2*pi*r*h. Total SA=2*pi*r(r+h). Volume=pi*r^2*h.
CONE: r=base radius, h=vertical height, l=slant height.
l=sqrt(r^2+h^2). Curved SA=pi*r*l. Total SA=pi*r(r+l). Volume=(1/3)*pi*r^2*h.
SPHERE: r=radius.
SA=4*pi*r^2. Volume=(4/3)*pi*r^3.
HEMISPHERE: r=radius.
Curved SA=2*pi*r^2. Total SA=3*pi*r^2. Volume=(2/3)*pi*r^3.
SOLVED EXAMPLES:
Example 1: Cone r=5cm, l=13cm.
h=sqrt(13^2-5^2)=sqrt(144)=12cm.
Curved SA=pi×5×13=65pi=204.1cm^2.
Total SA=pi×5×(5+13)=90pi=282.6cm^2.
Volume=(1/3)×pi×25×12=100pi=314.2cm^3.
Example 2: Sphere r=7cm.
SA=4×(22/7)×49=616cm^2.
Volume=(4/3)×(22/7)×343=1437.3cm^3.
Example 3: Cylinder r=4cm, h=10cm.
Curved SA=2×pi×4×10=80pi=251.2cm^2.
Volume=pi×16×10=160pi=502.4cm^3.
COMMON MISTAKES:
Cone: slant height l=sqrt(r^2+h^2). Given l, find h=sqrt(l^2-r^2).
Hemisphere Total SA=3pi*r^2 (curved 2pi*r^2 + base circle pi*r^2).
Volume of cone=(1/3)×volume of cylinder with same base and height.