A hemisphere ,a cylinder and a cone have equal radius and height.find the ratio of their curved surface area
Answers
Answered by
2
Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.
Then Curved surface area of Sphere= 4πr²
Curved surface area of cylinder = 2πr(2r) = 4πr²
Curved surface area of cone = πrl
where, l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5
⇒ Curved surface area of cone = π√5r2
Now,
Ratio of CSA 's a sphere ,cylinder and a cone = 4πr2:2πrh : πrl
= 4πr2:4πr2 : πr2√5
= 4 : 4 : √5
HOPE IT WILL HELP YOU
Then Curved surface area of Sphere= 4πr²
Curved surface area of cylinder = 2πr(2r) = 4πr²
Curved surface area of cone = πrl
where, l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5
⇒ Curved surface area of cone = π√5r2
Now,
Ratio of CSA 's a sphere ,cylinder and a cone = 4πr2:2πrh : πrl
= 4πr2:4πr2 : πr2√5
= 4 : 4 : √5
HOPE IT WILL HELP YOU
Similar questions
Math,
6 months ago
Computer Science,
6 months ago
English,
6 months ago
French,
11 months ago
Social Sciences,
11 months ago
Chemistry,
1 year ago
Biology,
1 year ago