Question

about surface area and volume

Answer 1

Wherever we look, usually we see solids. So far, in all our study, we have been dealing with figures that can be easily drawn on our notebooks or blackboards. These are called plane figures. We have understood what rectangles, squares and circles are, what we mean by their perimeters and areas, and how we can find them. We have learnt these in earlier classes. It would be interesting to see what happens if we cut out many of these plane figures of the same shape and size from cardboard sheet and stack them up in a vertical pile. By this process, we shall obtain some solid figures (briefly called solids) such as a cuboid, a cylinder, etc. In the earlier classes, you have also learnt to find the surface areas and volumes of cuboids, cubes and cylinders. We shall now learn to find the surface areas and volumes of cuboids and cylinders in details and extend this study to some other solids such as cones and spheres.

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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$\bf\Large\red{ THANKS \: FOR \: YOUR}$

$\bf\Large\red{ QUESTION \: HOPE \: IT }$

$\bf\Large\red{ HELPS }$

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