Question

if length is 10cm,breadth is 8cm and height is 6cm .then find L.s.a, T.s.a and volume of a cuboid?​

Answer 1

Answer:

L.s.a = 216 square cm

T.s.a = 376 square cm

valume of cuboid = 480 cubic cm

Answer 2

Answer:

${\large{\underline{\underline{\bf{Given \: : - }}}}}$

• ⟶ Lenght of cuboid = 10 cm
• ⟶ Breadth of cuboid = 8 cm
• ⟶ Height of cuboid = 6 cm

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{To \: Find\: : - }}}}}$

• ⟶ L.S.A of cuboid
• ⟶ T.S.A of cuboid
• ⟶ Volume of cuboid

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Using \: Formulae\: : - }}}}}$

• ⟶ L.S.A of cuboid = 2(l+b)h
• ⟶ T.S.A of cuboid = 2(lb+bh+hl)
• ⟶ Volume of cuboid (v) = lbh

$\green\bigstar$ Where

• ➱ L.S.A = Lateral surface area
• ➱ T.S.A = Total surface area
• ➱ l = Lenght
• ➱ b = Breadth
• ➱ h = Height
• ➱ v = Volume

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Solution\: : - }}}}}$

$\green\bigstar$ Finding lateral surface area of cuboid

${\dashrightarrow{\pmb{\sf{L.S.A \: of \: cuboid = 2(l + b)h}}}}$

• Substuting the values

${\dashrightarrow{\sf{L.S.A \: of \: cuboid = 2(10+ 8)6}}}$

${\dashrightarrow{\sf{L.S.A \: of \: cuboid = 2(18)6}}}$

${\dashrightarrow{\sf{L.S.A \: of \: cuboid = 2 \times 18 \times 6}}}$

${\dashrightarrow{\sf{L.S.A \: of \: cuboid = 216 \: {cm}^{2}}}}$

$\bigstar{\red{\underline{\boxed{\bf{L.S.A \: of \: cuboid = 216 \: {cm}^{2}}}}}}$

∴ The L.S.A of cuboid is 216 cm².

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Finding total surface area of cuboid

${\dashrightarrow{\pmb{\sf{T.S.A \: of \: cuboid = 2(lb + bh + hl)}}}}$

• Substuting the values

${\dashrightarrow{\sf{T.S.A \: of \: cuboid = 2(10 \times 8 + 8 \times 6 + 6 \times 10)}}}$

${\dashrightarrow{\sf{T.S.A \: of \: cuboid = 2(80 + 48 + 60)}}}$

${\dashrightarrow{\sf{T.S.A \: of \: cuboid = 2(188)}}}$

${\dashrightarrow{\sf{T.S.A \: of \: cuboid = 2 \times 188}}}$

${\dashrightarrow{\sf{T.S.A \: of \: cuboid = 376 \: {cm}^{2}}}}$

${\bigstar{\red{\underline{\boxed{\bf{T.S.A \: of \: cuboid = 376 \: {cm}^{2}}}}}}}$

∴ The T.S.A of cuboid is 376 cm².

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Finding volume of cuboid

${\dashrightarrow{\pmb{\sf{Volume \: of \: cuboid = lbh}}}}$

• Substuting the values

${\dashrightarrow{\sf{Volume \: of \: cuboid = 10 \times 8 \times 6}}}$

${\dashrightarrow{\sf{Volume \: of \: cuboid= 10 \times 48}}}$

${\dashrightarrow{\sf{Volume \: of \: cuboid = 480 \: {cm}^{3}}}}$

${\bigstar{\red{\underline{\boxed{\bf{Volume \: of \: cuboid = 480 \: {cm}^{3}}}}}}}$

∴ The volume of cuboid is 480 cm³.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Diagram\: : - }}}}}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf}\put(11.1,5.4){\bf}\put(11.2,9){\bf}\put(5.3,8.6){\bf}\put(3.3,10.2){\bf}\put(3.3,7){\bf}\put(9.25,10.35){\bf}\put(9.35,7.35){\bf}\put(3.5,6.1){\sf 8\:cm}\put(7.7,6.3){\sf 10\:cm}\put(11.3,7.45){\sf 6\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Learn \: More\: : - }}}}}$

• ⟶ Volume of cylinder = πr²h
• ⟶ T.S.A of cylinder = 2πrh + 2πr²
• ⟶ Volume of cone = ⅓ πr²h
• ⟶ C.S.A of cone = πrl
• ⟶ T.S.A of cone = πrl + πr²
• ⟶ Volume of cuboid = l × b × h
• ⟶ C.S.A of cuboid = 2(l + b)h
• ⟶ T.S.A of cuboid = 2(lb + bh + lh)
• ⟶ C.S.A of cube = 4a²
• ⟶ T.S.A of cube = 6a²
• ⟶ Volume of cube = a³
• ⟶ Volume of sphere = 4/3πr³
• ⟶ Surface area of sphere = 4πr²
• ⟶ Volume of hemisphere = ⅔ πr³
• ⟶ C.S.A of hemisphere = 2πr²
• ⟶ T.S.A of hemisphere = 3πr²

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Request\: : - }}}}}$

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