Home > Geometry > Perimeter and Area of Non-Standard Shapes

A cone has a height of #8 cm# and its base has a radius of #5 cm#. If the cone is horizontally cut into two segments #1 cm# from the base, what would the surface area of the bottom segment be?

Answer 1

#173.403\ \text{cm}^2#

Radius #r# of new circular section of bottom segment cut horizontally, at a height #h=1\ cm# from base, from an original cone of height #H=8\ cm# & base radius #R=5\ cm# is given by using property of similar triangles as follows

#\frac{R-r}{h}=\frac{R}{H}#

#r=R(1-\frac{h}{H})#

#=5(1-1/8)#

#=4.375\ cm#

Now, surface area of bottom segment of original cone

#=\text{area of circular top of radius 4.375 cm}+\text{curved surface area of frustum of cone}+\text{area of circular base of radius 5 cm}#

#=\pir^2+\pi(r+R)\sqrt{h^2+(R-r)^2}+\piR^2#

#=\pi(4.375)^2+\pi(4.375+5)\sqrt{1^2+(5-4.375)^2}+\pi(5)^2#

#=173.403\ \text{cm}^2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Theodore Abad

The surface area of the bottom segment of the cone, after it's horizontally cut 1 cm from the base, would be approximately 122.52 square centimeters.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.