Question

formula for area ,surface and volume of different shape

Answer 1

Answer:

Rectangle : Area = lb

Perimeter = 2(l+b)

Square : Area = a×a

Perimeter = 4a

Parallelogram: Area = l × h

Perimeter = 2(l+b)

Triangle : Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

Right angle Triangle : Area =1/2(bh)

Perimeter = b+h+d

Isosceles right angle triangle : Area = ½. a2

Perimeter = 2a+d……………………….where d=a√2

Equilateral Triangle : Area = √3. a2/4 or ½(ah)….where h = √3/2

Perimeter = 3a

Trapezium : Area = 1/2h(a+b)

Perimeter = Sum of all sides

Rhombus : Area = d1 × d2/2

Perimeter = 4l

Quadrilateral: Area =1/2 × Diagonal × (Sum of offsets)

Kite : Area = d1×d2/2

Perimeter = 2 × Sum on non-adjacent sides

Circle : Area = πr^2 or πd^2/4

Circumference = 2πr or πd

Area of sector of a circle = (θπr^2 )/360

Frustum : Curved surface area = πh(r1+r2)

Surface area = π( r12+ h(r1+r2) + r22)

Cube : Volume: V = l3

Lateral surface area = 4a2

Surface Area: S = 6s2

Diagonal (d) = √3l

Cuboid : Volume of cuboid: lbh

Total surface area = 2 (lb + bh + hl) or 6l2

Length of diagonal =√(l^2+b^2+h^2)

Right Circular Cylinder : Volume of Cylinder = π r2 h

Lateral Surface Area (LSA or CSA) = 2π r h

Total Surface Area = TSA = 2 π r (r + h)

Volume of hollow cylinder = π r h(R2 – r2)

Right Circular cone : Volume = 1/3 π r2h

Curved surface area: CSA= π r l

Total surface area = TSA = πr(r + l )

Sphere: Volume: V = 4/3 πr3

Surface Area: S = 4πr2

Hemisphere : Volume = 2/3 π r3

Curved surface area(CSA) = 2 π r2

Total surface area = TSA = 3 π r2

Prism : Volume = Base area x h

Lateral Surface area = perimeter of the base x h

Pyramid: Volume of a right pyramid = (1/3) × area of the base × height.

Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.

Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Tetrahedron : Area of its slant sides = 3a2√3/4

Area of its whole surface = √3a2

Volume of the tetrahedron = (√2/12) a 3

Regular Hexagon : Area = 3√3 a2 / 2

Perimeter = 6a

Some other Formula :

=Area of Pathway running across the middle of a rectangle = w(l+b-w)

=Perimeter of Pathway around a rectangle field = 2(l+b+4w)

=Area of Pathway around a rectangle field =2w(l+b+2w)

=Perimeter of Pathway inside a rectangle field =2(l+b-4w)

=Area of Pathway inside a rectangle field =2w(l+b-2w)

=Area of four walls = 2h(l+b)

Note : If we missed anything please mention it, we will update it

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

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

$\bf\Large\red{ HELPS }$

$\Large\mathcal\green{FOLLOW \: ME}$

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