Question 978640
If a cone's radius and slant height are halved, then how will the new surface area compare to the old surface area?
Simplify your answer and write it as a proper fraction or as a whole or mixed number.
The new surface area will be _____ times the old surface area.
:
Total surface area formula
{{{SA = (pi*r*s) + (pi*r^2)}}} where
r = the radius
s = the slant height
{{{SA = pi*r(s + r)}}}
:
let the original cone be 2r and 2s, half would be just r and s
cancel pi*r, then cancel (s+r)
{{{(pi*r(s + r))/(pi*2r(2s+2r))}}} = {{{(1(s + r))/(2(2s+2r))}}} = {{{(1(s + r))/(4(s+r))}}} = {{{1/4}}} of the old surface area