+26 1. The volume of a frustum of a right circular cone is 224π^3 its altitude is 6m and the sum of the radius of its bases is 12m, Find the radius of the larger base.
2.The frustum of a right circular cone has an altitude of 12 and the radii of the bases are 4cm and 9cm, Fidn the lateral area of the cone,
+130516 Here's 2
The lateral surface area is given by:
A = pi(R + r)L where R, r are the radiuses of the larger and smaller bases, respectively, and L is the length of the lateral side ...... and L = sqrt(h^2 + (R - r)^2) so we have
A = pi(9 + 4)sqrt(12^2 + (9 - 4)^2 ) = 13pi*sqrt(144 + 25) = 13pi* sqrt(169) = 13* pi * 13 =
169pi cm^2
Just a question on the 1st. part: aren't you missing two radii, both the top & bottom? you need the radius of the top to solve the radius of the base.No?.
+130516 Here's 1......
V = (pi * h)/3 * (R^2 + Rr + r^2) and we have
224pi^3 = [(pi * 6)/3] [R^2 + R(12-R) + (12- R)^2]
224 pi^2 = 2 [ R^2 + 12R - R^2 + 144 - 24R + R^2]
224pi^2 = 2 [R^2 - 12R + 144]
112pi^2 = [R^2 - 12R + 144] .....solving this equation for R we get that R ≈ 37.582
This is clearly impossible.....but.....I solved it based on the way you have written it........did you make a mistake somewhere???
[ Is 224pi^3 supposed to be something else???]
CPhill: I'm getting 64.00!!!!. Did you make a mistake by taking the volume as 224Pi^2 instead of 224Pi^3. I see that in your calculations.
+130516 Here's 2
The lateral surface area is given by:
A = pi(R + r)L where R, r are the radiuses of the larger and smaller bases, respectively, and L is the length of the lateral side ...... and L = sqrt(h^2 + (R - r)^2) so we have
A = pi(9 + 4)sqrt(12^2 + (9 - 4)^2 ) = 13pi*sqrt(144 + 25) = 13pi* sqrt(169) = 13* pi * 13 =
169pi cm^2
