Question

FORMULES OF SURFACE AREAS AND VOLUMES

Answer 1

CYLINDER
Volume:   V = r 2 h   Lateral Surface Area: LSA = 2r h 
(area of the "side" that surrounds the top and bottom circles)Total Surface Area:    TSA = 2r h + 2r 2 .=2r[r+h]
Volume:   Surface Area: SA = 4r 2[SPHERE]
cone:-
Volume = (1/3)πr2h
Slant Height = √(r2 + h2)Lateral Surface Area = πrs = πr√(r2 + h2)Total Surface Area
= L + B = πrl + πr2 =πr[l+r]frustum of the coneVolume = (1/3)πh (r12 + r22 + (r1 * r2))Slant Height = √((r1 - r2)2 + h2)LSA OF FRUSTUM -π(r1 + r2)lTSA OF FRUSTUM= πR²+πr²+π(r1 + r2)l
cuboid - tsa of cuboid-2[lb+bh+lh]
 lsa of cuboid=2h[l+b]
volume=lbh
 cube-
   tsa  of cube-6[side]²
lsa of cube=4[side]²
volume =[side]³

Answer 2

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

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$\Large\fbox{\color{purple}{QUESTION}}$

SURFACE AREA VOLUME FORMULAS

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$\Large\fbox{\color{purple}{ SOLUTION }}$

$\Large\mathcal\green{FRUSTUM}$

$\implies \: tsa = \pi \: l(r1 + r2) + \pi \: {r1}^{2} + \pi {r2}^{2}$

$\implies volume = \frac{1}{3}\pi \: h( {r1}^{2} + r1.r2 + {r2}^{2} )$

$\Large\mathcal\purple{CUBOID}$

$\implies \: lsa = 2(l + b)h \\ \\ \: \implies \: tsa = 2(lb + bl + hl) \\ \\ \implies \: volume \: = l \times b \times h$

$\Large\mathcal\blue{CUBE}$

$\implies \: lsa = {4a}^{2} \\ \\ \implies \: tsa = {6a}^{2} \\ \\ \implies \: volume = {a}^{3}$

$\Large\mathcal\brown{CYLINDER}$

$\implies \: csa = 2\pi \: r \: h \\ \\ \implies \: tsa = 2\pi \: r(r + h) \\ \\ \implies \: volume \: = \pi \: {r}^{2} h</p><p>$

$\Large\mathcal\orange{CONE}$

$\implies \: tsa \: = \: \pi \: r \: (l + r) \\ \\ \implies \: csa \: = \pi \: r \: l\\ \\ \implies \: volume \: = \frac{1}{3} (\pi \: {r}^{2} h)$

$\Large\mathcal\red {SPHERE }$

$\implies \: tsa \: = 4\pi \: {r}^{2} \\ \\ \implies \: csa \: = 4\pi \: {r}^{2} \\ \\ \implies \: volume \: = \frac{4}{3} \: {r}^{3}$

$\Large\mathcal\pink{HEMISPHERE}$

$\implies \: tsa \: =3\pi \: {r}^{2} \\ \\ \implies \: csa \: = 2\pi \: {r}^{2} \\ \\ \implies \: volume \: = \frac{2}{3} \pi \: {r}^{3}$

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