Question

Military tent of height 8.25 in the form of a right circular cylinder of base diameter 30 metre and height 5.5 surmounted by a right circular cone of the same radius find the length of the canvas using in making the 10th subject of the canvas is 1.5 metre

Answer 1

Military tent of height 8.25 in the form of a right circular cylinder of base diameter 30 metre and height 5.5 surmounted by a right circular cone of the same radius find the length of the canvas using in making the 10th subject of the canvas is 1.5 metre

Answer 2

Radius of cone = Radius of cylinder = $\sf{\frac{30}{2} m = 15m}$

Height of cylinder = 5.5m

Height of cone = 8.25 - 5.5 = 2.75m

Slant height of cone,

$\longrightarrow$ $\sf{l = \sqrt{ {(15)}^{2} + ({2.75)}^{2} } }$

$\longrightarrow$$\sf{ \sqrt{225 + 7.5625} m}$

$\longrightarrow$$\sf{\sqrt{232.5625} m}$

$\longrightarrow$$\sf{15.25m}$

Total area of canvas used = CSA of cylinder + CSA of cone

$\longrightarrow$$\sf{(2\pi \: \times 15 \times 5.5 + \pi \times 15 \times 15.25) {m}^{2}}$

$\longrightarrow$$\sf{15\pi(11 + 15.25) {m}^{2} = 15 \times 26.25\pi {m}^{2} }$

Length of canvas used = $\sf{\frac{Area}{Width}}$

$\longrightarrow$$\sf{\frac{15 \times 26.25\pi}{1.5}}$

$\longrightarrow$$\sf{262.5πm}$

$\longrightarrow$${\boxed{\sf{\red{824.25m}}}}$