If A1, A2 and A3 be the Surface Areas of a right circular cone, a sphere and a right circular cylinder, all having equal radii and equal heights and also radius is equal to the height, then A1 : A2 : A3 ?
1). 4: 4 : 3
2). 3 : 4 : 4
3). (1 + √2) : 4 : 4
4). 4 : 4 : ( 1 + √2)
We know that for a right circular cone, Slant height l = √(r2 + h2)
? Here r = h
⇒ l = r √2
Surface Area of a right circular cone(A1) = π r ( l + r)
⇒ π r (r √2 + r)
⇒ π r2(1 + √2)
Surface area of a sphere (A2) = 4 π r2
Surface Area of a right circular cylinder (A3) = 2 π r (r + h)
? Here r = h
⇒ A3 = 4 π r2
A1 : A2 : A3 = π r2 ( 1 + √2) : 4 π r2 : 4 π r2
⇒ ( 1 + √2) : 4 : 4