101. Find the length of the largest pole that can beplaced in a hall t

1.	101. Find the length of the largest pole that can beplaced in a hall that is 10 m long, 10 broad and4 m high.(a) 14.6 m (b) 18.6 m(c) 16.6 m (d) 20.20 m
Answer» $\large\underline{\sf{Given- }}$ Length of Hall, l = 10 m BREADTH of Hall, B = 10 m HEIGHT of hall, h = 4 m $\large\underline{\sf{To\:Find - }}$ Length of longest pole. $\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$ Let us CONSIDER a CUBOID having length l, breadth b and height h, then longest pole that can be placed in the cuboid is diagonal of cuboid, d given by $\boxed{ \sf \: Longest_{(pole)}=d \: = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2}}}$ $\large\underline{\sf{Solution-}}$ Given that Length of Hall, l = 10 m Breadth of Hall, b = 10 m Height of hall, h = 4 m So, Longest pole that can be placed in room is $\rm :\longmapsto\:Longest_{(pole)}=d = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} }$ $\rm :\longmapsto\:Longest_{(pole)}=d = \sqrt{ {(10)}^{2} + {(10)}^{2} + {(4)}^{2} }$ $\rm :\longmapsto\:Longest_{(pole)}=d = \sqrt{100 + 100 + 16}$ $\rm :\longmapsto\:Longest_{(pole)}=d = \sqrt{216}$ $\rm :\longmapsto\:Longest_{(pole)}=d = \sqrt{6 \times 6 \times 6}$ $\rm :\longmapsto\:Longest_{(pole)}=d = 6 \sqrt{6}$ $\rm :\longmapsto\:Longest_{(pole)}=d = 14.6 \: m$ $\bf \: Hence, \: Option \: (a) \: is \: correct.$ ─━─━─━─━─━─━─━─━─━─━─━─━─ Additional Information :- $\boxed{ \sf{ \: TSA{(cone)} = {6(edge)}^{2} }}$ $\boxed{ \sf{ \: TSA{(cuboid)} = 2(lb + bh + hl)}}$ $\boxed{ \sf{ \: TSA{(cone)} = \pi \: r(l + r)}}$ $\boxed{ \sf{ \: TSA{(cuboid)} = 2(lb + bh + hl)}}$ $\boxed{ \sf{ \: Volume_{(cube)} = {(edge)}^{3} }}$ $\boxed{ \sf{ \: Volume_{(cone)} = \dfrac{1}{3} \pi \: {r}^{2} h}}$ $\boxed{ \sf{ \: Volume_{(cuboid)} = lbh}}$ $\boxed{ \sf{ \: CSA{(cylinder)} = 2\pi \: rh}}$

101. Find the length of the largest pole that can beplaced in a hall that is 10 m long, 10 broad and4 m high.(a) 14.6 m (b) 18.6 m(c) 16.6 m (d) 20.20 m

Answer»

$\large\underline{\sf{Given- }}$

Length of Hall, l = 10 m

BREADTH of Hall, B = 10 m

HEIGHT of hall, h = 4 m

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

Length of longest pole.

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$

Let us CONSIDER a CUBOID having length l, breadth b and height h, then longest pole that can be placed in the cuboid is diagonal of cuboid, d given by

$\boxed{ \sf \: Longest_{(pole)}=d \: = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2}}}$