Find the area of a rectangular card board required to make a cylinder, with both ends open, of radius 1 3/4 dm and height 3 dm.
Answers
Given data :-
- Radius of cylinder ( r ) = 1 ⅓ dm
- Height of cylinder ( h ) = 3 dm
Solution:-
Now,
→ Area of cylinder = 2πr{h + r}
→ Area of cylinder = 2 × 22/7 × 1 ⅓ {3 + 1 ⅓}
→ Area of cylinder = 2 × 22/7 × 4/2 {3 + 4/3}
→ Area of cylinder = 176/7 {(9+4)/3}
→ Area of cylinder = 176/7 × 13/3
→ Area of cylinder = 2288/21
→ Area of cylinder = 108.9523dm²(approx)
Now, Area of two cirlcles of cylinder
→ Area of two cirlcles = 2{πr²}
→ Area of two cirlcles = 2{22/7 × (1 ⅓)² }
→ Area of two cirlcles = 2{22/7 × (4/3)²}
→ Area of two cirlcles = 2{22/7 × 16/9}
→ Area of two cirlcles = 2{352/63}
→ Area of two cirlcles = 2{5.5873}
→ Area of two cirlcles =11.1746dm²(approx)
→ Area of cylinder, with both ends open
= {Area of cylinder} - {Area of two cirlcles}
→ Area of cylinder, with both ends open
= 108.9523 - 11.1746
→ Area of cylinder, with both ends open
= 97.7777 dm²
We know that area of cylinder, with both ends open is know to be equal to area of a rectangular card board which required to make a cylinder, with both ends open.