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