Question

A cylindrical cake with a height of 5 inches has a 30 degree slice removed. If the volume of the removed slice is 40 inches what is the approximate radius of the cake

Answer 1

Answer: $5.52\ in.$

Step-by-step explanation:

Given

Height of cylindrical cake is $h=5\ in.$

$30^{\circ}$ slice is removed

Volume of the slice is $V=40\ in.^3$

Area of slice is

$\Rightarrow \dfrac{30^{\circ}}{360^{\circ}}\times \pi r^2\\\\\Rightarrow \dfrac{\pi r^2}{12}$

Volume of slice will be multiplication of area and height

$\Rightarrow V=A\times h\\\\\Rightarrow 40=\dfrac{\pi r^2}{12}\times 5\\\\\Rightarrow \pi r^2=\dfrac{40\times 12}{5}\\\\\Rightarrow r^2=\dfrac{40\times 12}{3.142\times 5}\\\\\Rightarrow r^2=30.55\\\Rightarrow r=5.52\ in.$

Hence, the radius of the cake is $5.52\ in.$