Answer :
well, the ratio of area is (Ratio of length)^2. So we work backwards.
ROL = [sqrt] 4:9
= 2:3
and its the same for height, because height is a length.
NB: Ratio of volume = (Ratio of length)^3
ROL = [sqrt] 4:9
= 2:3
and its the same for height, because height is a length.
NB: Ratio of volume = (Ratio of length)^3
Cone : r radius of bottom circle, L lateral length, h = perpendicular height
Total surface area = π r² ( 1 + L / r ) Volume = 1/3 π r² h
L² = r² + h²
Similar cones => r1 : r2 = L1: L2 = h1 : h2
=> L1 / r1 = L2 / r2 => 1+ L1/r1 = 1 + L2/r2
S1 : S2 = 2² : 3² = r1² : r2²
r1 : r2 = 2 : 3 also h1 : h2 = 2 : 3
Volumes V1 : V2 = r1² h1 / r2² h2 = (2/3)² 2/3 = 8 / 9
Total surface area = π r² ( 1 + L / r ) Volume = 1/3 π r² h
L² = r² + h²
Similar cones => r1 : r2 = L1: L2 = h1 : h2
=> L1 / r1 = L2 / r2 => 1+ L1/r1 = 1 + L2/r2
S1 : S2 = 2² : 3² = r1² : r2²
r1 : r2 = 2 : 3 also h1 : h2 = 2 : 3
Volumes V1 : V2 = r1² h1 / r2² h2 = (2/3)² 2/3 = 8 / 9
