What is the total surface area?
A hard-level "Area" problem.A curved surface flattens out if you cut it open: a cylinder's side becomes a rectangle, a cone's becomes a sector. In both, the width is the base's perimeter.
GivenA cylinder with base radius 3 cm and height 10 cm / π = 3.14
Hints
- A cylinder's surface has three parts: the top, the bottom and the side. Top and bottom are identical circles, each 3 × 3 × 3.14 = 28.26 cm².
- Here is the key. Cut the side open and it flattens into a rectangle. The curved surface has become a flat one.
- The rectangle's height is the cylinder's height, 10 cm. Its width is once round the base circle: 3 × 2 × 3.14 = 18.84 cm.
- So the side area is 18.84 × 10 = 188.4 cm². Once it is a rectangle it is plain multiplication.
- Top, bottom and side together: 28.26 × 2 + 188.4 = 244.92 cm².
Answer 244.92cm²
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?
Browse by idea
- Circles and sectors — multiply by π once, at the very end
- Flatten the solid before you think about it