please help me!!!
1. What is the ratio of the radii of two circles with area = 3 π square units and 75π square units?
b. What is the ratio of their circumferences?
2. What is the ratio of the sides of two trapezoids with area = 8 square units and 72 square units?
b. What is the ratio of their perimeters?
the areas grow as the square of the ratio of the radii
so, the radii and circumferences grow as the square root of the ratio of the areas, which is
3π / 75π = 1/25
So, the radii and circumferences have ratio 1/5
8/72 = 1/9
sides have ratio 1/3
The same logic applies to trapezoids.
Sure, I'd be happy to help you with these questions!
1. To find the ratio of the radii of two circles with given areas, you can follow these steps:
a. Start by finding the radii of the circles. The formula to find the radius (r) of a circle given its area (A) is: r = √(A/π). Using this formula, calculate the radii for both circles.
For the circle with an area of 3π square units, r₁ = √(3π/π) = √3.
For the circle with an area of 75π square units, r₂ = √(75π/π) = √75 = 5√3.
b. Now, calculate the ratio of the radii. Divide the larger radius (r₂) by the smaller radius (r₁): r₂/r₁.
In this case, the ratio of the radii is (5√3)/(√3) = 5.
So, the ratio of the radii of the two circles is 5:1.
c. Similarly, to find the ratio of their circumferences, you can use the formula C = 2πr, where C is the circumference and r is the radius.
For the circle with radius r₁, its circumference is C₁ = 2πr₁ = 2π(√3).
For the circle with radius r₂, its circumference is C₂ = 2πr₂ = 2π(5√3).
Now, calculate the ratio of the circumferences by dividing the larger circumference (C₂) by the smaller circumference (C₁): C₂/C₁.
The ratio of the circumferences will be (2π(5√3))/(2π(√3)) = 5.
So, the ratio of the circumferences of the two circles is also 5:1.
2. To find the ratio of the sides of two trapezoids with given areas, you can follow these steps:
a. Start by finding the lengths of the sides of the trapezoids. The formula to find the length of the side (s) of a trapezoid given its area (A) is: s = √(A/h), where h is the height of the trapezoid.
Using this formula, calculate the lengths of the sides for both trapezoids.
For the trapezoid with an area of 8 square units, let's assume its height is h₁. So, s₁ = √(8/h₁).
For the trapezoid with an area of 72 square units, let's assume its height is h₂. So, s₂ = √(72/h₂).
b. Now, calculate the ratio of the sides. Divide the larger side length (s₂) by the smaller side length (s₁): s₂/s₁.
In this case, the ratio of the sides is (√(72/h₂))/(√(8/h₁)).
Please provide the height values (h₁ and h₂) for the respective trapezoids in order to calculate the exact ratio of their sides.
c. Similarly, to find the ratio of their perimeters, you can sum up all the sides of the trapezoids.
For the trapezoid with side lengths s₁, let's assume the other two side lengths as a₁ and b₁. So, the perimeter P₁ = a₁ + b₁ + 2s₁.
For the trapezoid with side lengths s₂, let's assume the other two side lengths as a₂ and b₂. So, the perimeter P₂ = a₂ + b₂ + 2s₂.
Now, calculate the ratio of the perimeters by dividing the larger perimeter (P₂) by the smaller perimeter (P₁): P₂/P₁.
Again, please provide the values of the other two side lengths (a₁, a₂, b₁, and b₂) for the respective trapezoids in order to calculate the exact ratio of their perimeters.
I hope this helps! If you have any more questions, feel free to ask.