A cone has a height of #12 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?
1 Answer
The total surface area of the bottom segment is
Explanation:
Calculate the base area
Calculate the original sloping surface area
The formula for the sloping surface of a right cone is
For the current cone
The original surface area is
Calculate the new base radius
the height and the radius of the base give a right angled triangle with angle
equation 1:
After the cut,
The new height is 9cm (
let the new base radius be
equation 2 :
Using equation 1 and equation 2 to eliminate
The new top radius is 3cm
Calculate the top surface of the bottom section
Using
calculate the sloping surface of the new cone
The new cone has a sloping surface area of
Calculating the sloping surface area of the bottom section
Therefore the bottom section has a sloping surface area of
The total surface area is original base area + top area + sloping surface