Final answer:
To find out how many triangles can fit inside a circle with 5 times the radius of the given circle, we can compare the areas of the two circles. We find that you can fit approximately 314 triangles inside the circle that is 5 times bigger in radius compared to the given circle.
Step-by-step explanation:
To find out how many triangles can fit inside a circle with 5 times the radius of the given circle, we need to compare the areas of the two circles. The area of the given circle is 64 cm². Since the area of a circle is given by the formula A = πr², we can use this formula to find the radius of the given circle.
Given that the base of the triangle is 4 cm and the height is 2 cm, the area of the triangle is 1/2 × base × height = 1/2 × 4 cm × 2 cm = 4 cm².
Now, let's calculate the radius of the given circle: A = πr², 64 cm² = πr². Solving for r, we get r = √(64/π) ≈ 4 cm.
The radius of the bigger circle is 5 times the radius of the given circle, which means r = 4 cm × 5 = 20 cm. To find the area of the bigger circle, A = π(20 cm)² = 400π cm² ≈ 1256 cm². Now, we can find how many triangles can fit inside the bigger circle by dividing the area of the bigger circle by the area of one triangle: 1256 cm² ÷ 4 cm² = 314. Therefore, you can fit approximately 314 triangles inside the circle that is 5 times bigger in radius compared to the given circle.