Question

Из железной полосы длиной L метров нужно изготовить обруч. На соединение концов уходит D метров полосы. Разработать схему алгоритма для вычисления радиуса R обруча. Протестировать алгоритм для а) L=5.8, D=0.2, б) L=3.25, D=0.1

Answer 1

$L=D+ \pi r^{2}$
$\pi r^{2} =L-D$
$r^{2} = \frac{L-D}{ \pi }$
$r = \sqrt{ \frac{L-D}{ \pi } }$
function r(l, d: real):real;
begin
  result:=sqrt((l-d)/pi);
end;
var l, d: real;
begin
  l:=5.8;
 d:=0.2;
  writeln('L = ', l, ' D = ', d, ' r = ', r(l, d));
  l:=3.25; d:=0.1;
  writeln('L = ', l, ' D = ', d, ' r = ', r(l, d));
end.

Answer 2

Problem Analysis

To calculate the radius of the hoop, we need to consider the length of the iron strip (L) and the amount of strip used for joining the ends (D). The formula for calculating the radius (R) of the hoop can be derived using the circumference formula:

C = 2πR

Given that the length of the iron strip is L and the amount used for joining the ends is D, we can write the equation:

L = C + D

Substituting the value of C from the circumference formula, we get:

L = 2πR + D

Solving this equation for R will give us the radius of the hoop.

Algorithm

1. Read the values of L and D. 2. Calculate the radius R using the formula R = (L - D) / (2π). 3. Print the value of R.

Pseudocode

``` Read L, D R = (L - D) / (2 * π) Print R ```

Testing the Algorithm

a) For L = 5.8 and D = 0.2: ``` L = 5.8, D = 0.2 R = (5.8 - 0.2) / (2 * π) ≈ 0.915 ``` b) For L = 3.25 and D = 0.1: ``` L = 3.25, D = 0.1 R = (3.25 - 0.1) / (2 * π) ≈ 0.514 ```

Please note that the values of π used in the calculations are approximate.

Let me know if you need any further assistance!