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=asqrt(3). CYLINDER: r=radius, h=height. Curved SA=2pirh. Total SA=2pir(r+h). Volume=pir^2h. CONE: r=base radius, h=vertical height, l=slant height. l=sqrt(r^2+h^2). Curved SA=pirl. Total SA=pir(r+l). Volume=(1/3)pir^2h. SPHERE: r=radius. SA=4pir^2. Volume=(4/3)pir^3. HEMISPHERE: r=radius. Curved SA=2pir^2. Total SA=3pir^2. Volume=(2/3)pir^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=3pir^2 (curved 2pir^2 + base circle pi*r^2). Volume of cone=(1/3)×volume of cylinder with same base and height.