How long is the whole spiral?
A normal-level "Length" problem.Multiply by π once, at the very end. Adding the radii first makes the arithmetic lighter and much harder to get wrong.
GivenSemicircles of radius 1 cm, 2 cm, 3 cm, 4 cm are joined as shown / π = 3.14
Hints
- It looks like one curve, but at the marked points it breaks into 4 semicircles. Find each length, then add.
- A semicircle's arc is half a circumference: diameter × 3.14 ÷ 2, which is simply radius × 3.14.
- So each one is 1×3.14, 2×3.14, 3×3.14, 4×3.14. You could add these up — but there is a faster route.
- Every term has the form "radius × 3.14", so factor the 3.14 out: (1 ＋ 2 ＋ 3 ＋ 4) × 3.14 = 10 × 3.14. One multiplication by π instead of 4.
- The answer is 31.4 cm. However many semicircles there are, just add all the radii, then multiply by 3.14 once.
Answer 31.4cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How deep was the water?