Question

formulas of surface area and volume class 9

Answer 1

CUBOID
Base area = lb
Base perimeter =2(l+b)
Volume = l b h
L.S.A = 2(l+b) x h
T.S.A = 2(lb + bh + lh)
Sum of all edges = 4 (l+b+h)
Diagonal length = √l² +b²+h²

CUBE
Base area = a²
Base perimeter = 4a
Volume = a³
L.S.A = 4 a²
T.S.A = 6 a ²
Sum of all edges = 12 a
Diagonal = √3 a

CYLINDER

Base area =π r²
Base perimeter = 2 π r
Volume = π r² h
C.S.A = 2 π r h
T.S.A = 2 π r ( r +h )

CYLINDRICAL PIPE

Base area = π (R² - r² )
Volume = π (R² - r² ) × h
Outer C.S.A = 2 π R h
Inner C.S.A = 2 π r h

CIRCULAR RING
Area = π (R² - r² )

CONE
Base area = π r ²
Base perimeter = 2 π r
Volume = 1/3 π r² h
C.S.A = π r l
T.S.A = πr (r + l)

SPHERE
Surface area = 4 π r ²
Volume = 4/3 π r ³

SPHERICAL SHELL:If R is the outer radius and r is the inner radius , then
Volume = 4/3 π (R³ - r³)

HEMISPHERE
Base area = π r ²
C.SA. = 2 π r ²
T.S.A = 3π r ²
Volume = 2/3 π r ³

HEMISPHERICAL SHELL

Base area = π (R² - r²)
Volume = 2/3 π(R³ - r ³)
Inner C.S.A = 2π r²
Outer C.S.A = 2πR²
T.S.A = π (R² - r²)+2π r²+2πR²

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

$\Large\mathcal\purple{CUBOID}$

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

$\Large\mathcal\blue{CUBE}$

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

$\Large\mathcal\brown{CYLINDER}$

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

$\Large\mathcal\orange{CONE}$

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

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