Answer: [tex]5.52\ in.[/tex]
Step-by-step explanation:
Given
Height of cylindrical cake is [tex]h=5\ in.[/tex]
[tex]30^{\circ}[/tex] slice is removed
Volume of the slice is [tex]V=40\ in.^3[/tex]
Area of slice is
[tex]\Rightarrow \dfrac{30^{\circ}}{360^{\circ}}\times \pi r^2\\\\\Rightarrow \dfrac{\pi r^2}{12}[/tex]
Volume of slice will be multiplication of area and height
[tex]\Rightarrow V=A\times h\\\\\Rightarrow 40=\dfrac{\pi r^2}{12}\times 5\\\\\Rightarrow \pi r^2=\dfrac{40\times 12}{5}\\\\\Rightarrow r^2=\dfrac{40\times 12}{3.142\times 5}\\\\\Rightarrow r^2=30.55\\\Rightarrow r=5.52\ in.[/tex]
Hence, the radius of the cake is [tex]5.52\ in.[/tex]
