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.`

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 (30^(\circ))/(360^(\circ))* \pi r^2\\\\\Rightarrow (\pi r^2)/(12)`

Volume of slice will be multiplication of area and height

`\Rightarrow V=A* h\\\\\Rightarrow 40=(\pi r^2)/(12)* 5\\\\\Rightarrow \pi r^2=(40* 12)/(5)\\\\\Rightarrow r^2=(40* 12)/(3.142* 5)\\\\\Rightarrow r^2=30.55\\\Rightarrow r=5.52\ in.`

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