A military tent of height 8.25m …

Given Height of the tent (h) = 8.25 m.
Diameter of cylindrical base = 30 m
{tex}\Rightarrow{/tex} Radius of cylindrical base (r) = Radius of the cone = 15 m,
Height of cylinder = 5.5 m
Height of cone (h) = Height of the tent - Height of the cylinder
= 8.25 - 5.5
= 2.75 m
Slant height of cone, l {tex}= \sqrt { r ^ { 2 } + h ^ { 2 } }{/tex}
{tex}= \sqrt { ( 15 ) ^ { 2 } + ( 2.75 ) ^ { 2 } }{/tex}
{tex}= \sqrt { 225 + 7.5625 }{/tex}
{tex}= \sqrt { 232.5625 }{/tex}
= 15.25 m
Total surface area of the tent = Curved surface area of cone + Curved surface area of cylinder
= {tex}\pi r l + 2 \pi r h{/tex}
{tex}= \pi r ( l + 2 h ){/tex}
{tex}= \frac { 22 } { 7 } \times 15 ( 15.25 + 2 \times 5.5 ){/tex}
{tex}= \frac { 22 } { 7 } \times 15 \times 26.25{/tex}
= 1237.5 m²
Now, breadth of the canvas (b) = 1.5 m
Let the length of the canvas = a m
Area of the canvas = Total surface area of the tent
{tex}\Rightarrow{/tex} a {tex}\times{/tex} b = 1237.5
{tex}\Rightarrow{/tex} a {tex}\times{/tex} 1.5 = 1237.5
{tex}\Rightarrow{/tex} a = 825 m
Thus, length of the canvas is 825 m.