Question

List all the important formulae from Ch: Surface Areas & Volumes [Class 9 CBSE]

Answer 1

Hey There, A Good & Important Question! ☺

Formulae are something we have to learn thoroughly in this chapter. We need them to solve every question from this lesson.

So, I'll list down the important formulae from this lesson which will be helpful to all 9th graders... ☺


                                                               Formulae

Cuboid :

Total Surface Area (T.S.A) = 2 [ lb+ bh+ hl ]
Lateral Surface Area (C.S.A) = 2 [ bh + hl ]
Perimeter of a Cuboid = 4 [ l + b + h ]
Volume = lbh

Cube :

T.S.A = 6a²
C.S.A = 4a²
Perimeter = 12a
Volume = a³

Special Cases [Rooms] :

Area of 4 walls + ceiling or floor = lb + 2 [ bh + hl ]

Cylinder :

C.S.A = 2 $\pi$rh
T.S.A = 2 $\pi$r (r + h)
Volume = $\pi$r²h

Hollow Cylinder :

Let R and r be the external and internal radii of a hollow cylinder of height h

C.S.A = 2 $\pi$rh [ R + r ]
T.S.A = 2 $\pi$ [ R + r ] [ h + R - r ]
Volume = $\pi$ [ R² - r² ] h

Cone :

base radius → r , slant height → l , height → h
l² = r² + h²

C.S.A = $\pi rl$
T.S.A = $\pi r ( r + l )$
Volume = $\frac{1}{3} \pi$r²h

Sphere :

Surface Area = 4 $\pi r^{2}$
Volume = $\frac{4}{3}$ $\pi r^{3}$

Hemi-sphere :

C.S.A = 2 $\pi r^{2}$
T.S.A = 3 $\pi r^{2}$
Volume = $\frac{2}{3} \pi r^{3}$

Spherical Shell :

Volume of a spherical shell whose outer and inner radii are R & r respectively

V = $\frac{4}{3} \pi$ [ R³ - r³ ]


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These are the important formaule from the lesson. I hope it would help all to learn this chapter at ease... ☺☻☺

Answer 2

1.) SA of cuboid - 2( lb+BH+hl )
2.)SA of cube - 6a²
3.) CSA of cylinder- 2πrh
4.) TSA of cylinder - 2πr ( r+h )
5.) CSA of cone - πrl
6.) TSA of right circular cone - πr ( l+r )
7.) SA of sphere - 4πr²
8.) CSA of a hemisphere - 2πr
9.) TSA of hemisphere - 3πr²
10.) Volume of cuboid - lbh
11.) Volume if cube - a³
12.) Volume of cylinder - πr²h
13.) Volume of cone - 1/3πr²h
14.) Volume of sphere - 4/3 πr³
15.) Volume of hemisphere - 2/3 πr³
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Hope it helps : )