Answer to Question #187579 in Geometry for John

Question

The uniform cross section of a cabin storage compartment on a jet plane is a sector of a circle with radius 55cm, and angle Ө c .  The container is 96 cm wide. The volume of the container is 0.2178 m3. What is the angle Өc

Answer 1

We have given that,

$r= 55cm = 0.55m$

Length of wide $= 96cm = 0.96m$

Volume = $0.2178 m^3$

$\theta_c$ = ?

We know volume of the sector

$= \dfrac{\theta_c \times \pi r^2}{360} \times length$

$0.2178 = \dfrac{\theta_c\times 3.14 \times 0.55 \times 0.55}{360} \times 0.96$

$\theta_c = \dfrac{78.408}{0.911} = 86.06$