if the surface area of a sphere is increases by 44%, find the %increase in its diameter

Answer 1

Surface Area of a Sphere (A) = 4πr ²

Area is directly proportional to r². So, A₂/A₁ = r ₂²/ r ₁²

Area increased by 44% of its original area. So, A2 = 1.44A1

A₂/A₁ = r ₂²/ r ₁²

1.44/1 = r ₂²/ r ₁²

r ₂² = 1.44 r ₁²

Take square root each side

r ₂ = sqrt(1.44) r ₁

r ₂ = 1.2 r ₁ = r ₁ + 0.2 r ₁

% increase in it's diameter is 20%.