Question

3. The lateral surface area of the cuboid is 200 m². Its length and breadth are 15m, 10m
respectively. Then the height is
(A) 5 cm
(B) 10 m
(C) 4 m
(D) 15 m​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given\::- }}}}$

• Lateral Surface Area of cuboid = 200m².

• Length of cuboid = 15m

• Breadth of cuboid = 10m

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To \: find\::- }}}}$

• Height of cuboid.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Formula\::- }}}}$

$\large\sf\green{lateral \: surface \: of \:cuboid = 2h(l +b) }$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution \::- }}}}$

$\dashrightarrow\qquad\sf Lateral \: surface \: area \: of \: cuboid = 200m^2$

$\dashrightarrow\qquad\sf Length \: of \: cuboid = 15m$

$\dashrightarrow\qquad\sf Breadth \: of \: cuboid = 10m$

$\dashrightarrow\qquad\sf According \:to \: formula ,$

$\dashrightarrow\qquad\sf 200 = 2h(l+b)$

$\dashrightarrow\qquad\sf 200 = 2h(15+10)$

$\dashrightarrow\qquad\sf 2h(25) = 200$

$\dashrightarrow\qquad\sf h\times 25 = \dfrac{200}{2}$

$\dashrightarrow\qquad\sf h \times 25 = 100$

$\dashrightarrow\qquad\sf h = \dfrac{100}{25}$

$\dashrightarrow\qquad\sf h = 4m$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Therefore,\::- }}}}$

$\large\sf\green{Height \: of \: cuboid = 4m}$

Answer 2

Answer:

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Given:}}}}}}}\end{gathered}$

• $\red\bigstar$ Lateral surface area of cuboid = 200 m²
• $\red\bigstar$ Lenght of cuboid = 15 m
• $\red\bigstar$ Breadth of Cuboid = 10 m

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{To Find:}}}}}}}\end{gathered}$

• $\red\bigstar$ Height of cuboid

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Using Formula:}}}}}}}\end{gathered}$

$\dag{\underline{\boxed{\sf{LSA \: of \: cuboid \: = \: 2h(l+b)}}}}$

Where

• $\green\star$ LSA of cuboid = Lateral Surface Area of cuboid
• $\green\star$ H = Height of cuboid
• $\green\star$ L = Lenght of cuboid
• $\green\star$ B = Breadth of cuboid

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Solution:}}}}}}}\end{gathered}$

$\quad {: \implies{\sf{LSA \: of \: cuboid = \bf{2h(l+b)}}}}$

• Substituting the values

$\quad {: \implies{\sf{200= \bf{2h(15+10)}}}}$

$\quad {: \implies{\sf{200= \bf{2h(25)}}}}$

$\quad {: \implies{\sf{\dfrac{200}{2}}} = \bf{h \times 25}}$

$\quad {: \implies{\sf{\cancel{\dfrac{200}{2}}}} = \bf{h \times 25}}$

$\quad {: \implies{\sf{100}} = \bf{h \times 25}}$

$\quad {: \implies{\sf{\dfrac{100}{25}}} = \bf{h}}$

$\quad {: \implies{\sf{\cancel{\dfrac{100}{25}}}} = \bf{h}}$

$\quad {: \implies{\sf{4 \: m}} = \bf{h}}$

$\quad\dag{\underline{\boxed{\sf{Height = 4 \: m}}}}$

• Henceforth,The height of cuboid is 4 m.

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Verification:}}}}}}}\end{gathered}$

$\quad {: \implies{\sf{LSA \: of \: cuboid = \bf{2h(l+b)}}}}$

• Substituting the values

$\quad {: \implies{\sf{200 \: {m}^{2} = \bf{2 \times 4(15 + 10)}}}}$

$\quad {: \implies{\sf{200 \: {m}^{2} = \bf{8(25)}}}}$

$\quad {: \implies{\sf{200 \: {m}^{2} = \bf{8 \times 25}}}}$

$\quad {: \implies{\sf{200 \: {m}^{2} = \bf{200 \: {m}^{2} }}}}$

$\quad\dag{\underline{\boxed{\sf{LHS=RHS}}}}$

• Hence Verified!!

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Diagram:}}}}}}}\end{gathered}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf }\put(11.1,5.4){\bf }\put(11.2,9){\bf }\put(5.3,8.6){\bf }\put(3.3,10.2){\bf }\put(3.3,7){\bf }\put(9.25,10.35){\bf }\put(9.35,7.35){\bf }\put(3.5,6.1){\sf 10\:m}\put(7.7,6.3){\sf 15\:m}\put(11.3,7.45){\sf 4\:m}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

• See the diagram from website Brainly.in.

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

$\begin{gathered}{\large{\textsf{\textbf{\underline{\underline{\color{blue}{Learn More:}}}}}}}\end{gathered}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: cuboid \: = \: 2(l \times b + b \times h + l \times h)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto LSA \: of \: cuboid \: = \: 2h(l+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cuboid \: = \: L \times B \times H}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diagonal \: of \: cuboid \: = \: \sqrt 3l}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: cuboid \: = \: 12 \times Sides}}}$