Question

Formula of surface area and volume​

Answer 1

AnswEr :

$\huge{\underline{\boxed{\frak \orange{Formulae \: of \: Cube :-}}}}$

⋆Reference of image is shown in Diagram

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$\scriptsize\sf{\quad\dag\ Here, \: a \: is \: side}$

$\normalsize\dashrightarrow\sf\ Lateral \: surface \: area \: of \: cube = 4a^{2}$

$\normalsize\dashrightarrow\sf\ Total \: surface \: area \: of \: cube = 6a^{2}$

$\normalsize\dashrightarrow\sf\ Volume \: of \: cube = a^{3}$

$\normalsize\dashrightarrow\sf\ Diagnol \: of \: cube = \sqrt{3a}$

$\huge{\underline{\boxed{\frak \red{Formulae \: of \: Cuboid :-}}}}$

⋆Reference of image is shown in diagram

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$\scriptsize\sf{\quad\dag\ L = Length}$

$\scriptsize\sf{\quad\dag\ B = Breadth}$

$\scriptsize\sf{\quad\dag\ H = Height}$

$\normalsize\dashrightarrow\sf\ Lateral \: surface \: area \: of \: cuboid = 2(L + B)H$

$\normalsize\dashrightarrow\sf\ Total \: surface \: area \: of \: cuboid = 2(LB + BH + HL)$

$\normalsize\dashrightarrow\sf\ Volume \: of \: cuboid = L \times\ B \times\ H$

$\normalsize\dashrightarrow\sf\ Diagnol \: of \: cuboid = \sqrt{L + B + H}$

$\huge{\underline{\boxed{\frak \pink{Formulae \: of \: Cylinder:- }}}}$

⋆Reference of image in shown in diagram

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$\scriptsize\sf{\quad\dag\ r = Radius }$

$\scriptsize\sf{\quad\dag\ H = Height}$

$\normalsize\dashrightarrow\sf\ Lateral \: surface \: area \: of \: cylinder = 2 \pi rh$

$\normalsize\dashrightarrow\sf\ Total \: surface \: area \: of \: cylinder = 2 \pi r [r + h]$

$\normalsize\dashrightarrow\sf\ Volume \: of \: cylinder = 2 \pi rh$

$\huge{\underline{\boxed{\frak \green{Formulae \: of \: cone :-}}}}$

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$\scriptsize\sf{\quad\dag\ r = Radius}$

$\scriptsize\sf{\quad\dag\ l = slant \: height}$

$\scriptsize\sf{\quad\dag\ h = Height}$

$\normalsize\dashrightarrow\sf\ Lateral \: surface \: area \: of \: cone = \pi rl$

$\normalsize\dashrightarrow\sf\ Total \: surface \: area \: of \: cone = \pi r[r + l]$

$\normalsize\dashrightarrow\sf\ Volume \: of \: cone = \frac{1}{3} \pi r^2h$

$\normalsize\dashrightarrow\sf\ slant \: height\: of \: cone(l) = \sqrt{r^{2} + h^{2} }$

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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