A rectangle wother does 12 and 16 cm is inscribed in a circle with centre of.a dart is thrown and lands in the interior of circle what is its probability of dart that lands in the shaded region
Don't understand your word salad, but it looks like you have a rectangle with a circle in it.
No idea where the shaded region is, but ...
find the area of the rectangle
find the area of the circle
Assuming the shaded region is the part outside the circle within the rectangle, you can now find the area of that
Prob(of whatever you are asking for)
= area of shaded region/ area of rectangle
To find the probability of a dart landing in the shaded region, we need to compare the area of the shaded region to the total area of the circle.
Let's start by finding the area of the rectangle. The rectangle with width 12 cm and height 16 cm has an area of 12 cm * 16 cm = 192 cm².
Next, let's find the diameter of the circle. Since the rectangle is inscribed in the circle, the diameter of the circle is equal to the diagonal of the rectangle. Using the Pythagorean theorem, we can find the diagonal:
diagonal² = width² + height²
diagonal² = 12² + 16²
diagonal² = 144 + 256
diagonal² = 400
diagonal = √400
diagonal = 20 cm
Now that we know the diameter of the circle is 20 cm, we can find its radius. The radius is half the diameter, so the radius of the circle is 20 cm / 2 = 10 cm.
The area of the circle is given by the formula A = πr², where r is the radius of the circle. Therefore, the area of the circle is A = π(10 cm)² = 100π cm².
Finally, let's find the area of the shaded region. Since the rectangle is inscribed in the circle, the shaded region is the difference between the area of the circle and the area of the rectangle:
Shaded area = Area of circle - Area of rectangle
Shaded area = 100π cm² - 192 cm²
Now we can calculate the probability of the dart landing in the shaded region:
Probability = Shaded area / Total area
Probability = (100π cm² - 192 cm²) / (100π cm²)
Simplifying this expression might be difficult, as we have an irrational number (π) involved. However, we can approximate the probability by using a numerical value for π, such as 3.14 or 3.14159.
So, the probability of the dart landing in the shaded region is approximately:
Probability ≈ (100 * 3.14 cm² - 192 cm²) / (100 * 3.14 cm²)
This final calculation will give you the estimated probability, taking into account the given dimensions and assuming a value for π.